WEBVTT 00:00:00.000 --> 00:00:01.964 align:middle line:90% [SQUEAKING] 00:00:01.964 --> 00:00:03.928 align:middle line:90% [RUSTLING] 00:00:03.928 --> 00:00:05.892 align:middle line:90% [CLICKING] 00:00:05.892 --> 00:00:16.510 align:middle line:90% 00:00:16.510 --> 00:00:18.800 align:middle line:84% GLENN ELLISON: OK, so let me get started. 00:00:18.800 --> 00:00:21.380 align:middle line:84% Today I'm going to be talking about auctions. 00:00:21.380 --> 00:00:24.220 align:middle line:84% And let me say that this lecture is going to be-- 00:00:24.220 --> 00:00:26.350 align:middle line:84% there's a lot of math on the slides. 00:00:26.350 --> 00:00:29.470 align:middle line:84% I like to have lectures where you watch everything 00:00:29.470 --> 00:00:30.387 align:middle line:90% and you understand it. 00:00:30.387 --> 00:00:32.387 align:middle line:84% Today there are going to be some of those slides 00:00:32.387 --> 00:00:34.573 align:middle line:84% that you just look at them at home afterwards 00:00:34.573 --> 00:00:36.740 align:middle line:84% to try to get how I'm doing some of the derivations. 00:00:36.740 --> 00:00:41.565 align:middle line:84% But anyway, we're used to and I think almost all this class, 00:00:41.565 --> 00:00:42.940 align:middle line:84% we've been of talking about firms 00:00:42.940 --> 00:00:44.590 align:middle line:84% and the firms have been setting prices 00:00:44.590 --> 00:00:46.210 align:middle line:84% and the firms have been setting prices 00:00:46.210 --> 00:00:50.380 align:middle line:84% to maximize profits or some kind of oligopoly competition. 00:00:50.380 --> 00:00:52.420 align:middle line:84% There are many real world applications 00:00:52.420 --> 00:00:55.430 align:middle line:90% where firms do not set prices. 00:00:55.430 --> 00:01:04.930 align:middle line:84% And instead, firms use auctions as a mechanism to set prices. 00:01:04.930 --> 00:01:08.080 align:middle line:84% Three of the biggest applications. 00:01:08.080 --> 00:01:09.760 align:middle line:90% Government procurement. 00:01:09.760 --> 00:01:11.920 align:middle line:84% Whenever the government is hiring contractors 00:01:11.920 --> 00:01:14.920 align:middle line:84% to pave roads or fix bridges or things like that, 00:01:14.920 --> 00:01:17.180 align:middle line:84% these are usually done through procurement auctions 00:01:17.180 --> 00:01:19.850 align:middle line:84% where the government asks firms to submit bids for how much they 00:01:19.850 --> 00:01:21.990 align:middle line:84% would need to charge to pave a road 00:01:21.990 --> 00:01:27.140 align:middle line:84% and then choose the winning bidder to be the lowest bidder. 00:01:27.140 --> 00:01:31.130 align:middle line:84% In financial markets, the US auctions Treasury bills. 00:01:31.130 --> 00:01:33.068 align:middle line:84% And Treasury bills are trillions of dollars, 00:01:33.068 --> 00:01:34.610 align:middle line:84% and so there are trillions of dollars 00:01:34.610 --> 00:01:37.730 align:middle line:90% in auctions and that thing. 00:01:37.730 --> 00:01:42.650 align:middle line:84% Online advertising is also absolutely enormous. 00:01:42.650 --> 00:01:45.110 align:middle line:84% Every time you're looking at a computer screen 00:01:45.110 --> 00:01:47.630 align:middle line:84% and you see some ads on the page or whatever, 00:01:47.630 --> 00:01:50.690 align:middle line:84% whether it's a news site or a search engine 00:01:50.690 --> 00:01:52.623 align:middle line:84% or whatever, almost all of those ads 00:01:52.623 --> 00:01:55.040 align:middle line:84% these days are being auctioned off rather than being sold, 00:01:55.040 --> 00:01:57.570 align:middle line:84% because it's just very hard to know what the price is. 00:01:57.570 --> 00:01:59.570 align:middle line:84% What is it worth to show you an ad 00:01:59.570 --> 00:02:00.875 align:middle line:90% at a particular point in time? 00:02:00.875 --> 00:02:02.250 align:middle line:84% And so there's auction mechanisms 00:02:02.250 --> 00:02:05.450 align:middle line:90% that are setting the prices. 00:02:05.450 --> 00:02:09.740 align:middle line:84% There have been lots of academic research 00:02:09.740 --> 00:02:10.952 align:middle line:90% in the past few decades. 00:02:10.952 --> 00:02:13.160 align:middle line:84% I think one of the reasons why people in IO like this 00:02:13.160 --> 00:02:16.970 align:middle line:84% is because we always like to write down models and have 00:02:16.970 --> 00:02:19.388 align:middle line:84% these mathematical models that shed clarity on something. 00:02:19.388 --> 00:02:20.930 align:middle line:84% And often in many other applications, 00:02:20.930 --> 00:02:23.240 align:middle line:84% we're making up the model and making up the game 00:02:23.240 --> 00:02:24.410 align:middle line:90% that people are playing. 00:02:24.410 --> 00:02:27.170 align:middle line:84% In auctions, it's very clear that there is a real game 00:02:27.170 --> 00:02:29.370 align:middle line:84% and you can see the game that people are playing. 00:02:29.370 --> 00:02:32.000 align:middle line:84% It helps you do this nice connection between theory 00:02:32.000 --> 00:02:32.960 align:middle line:90% and empirics. 00:02:32.960 --> 00:02:39.620 align:middle line:84% And in terms of what's happened in IO, this really grew in the-- 00:02:39.620 --> 00:02:45.890 align:middle line:84% I guess that was in the 1990s or early 2000s when formally 00:02:45.890 --> 00:02:49.520 align:middle line:84% the airwaves that are used for cell phone signals and for TV 00:02:49.520 --> 00:02:51.982 align:middle line:84% licenses and things like that, in the old days, 00:02:51.982 --> 00:02:53.940 align:middle line:84% those were simply given away by the government. 00:02:53.940 --> 00:02:56.570 align:middle line:84% And if the government gave you one of the three licenses 00:02:56.570 --> 00:02:59.180 align:middle line:84% to conduct television in a city, you 00:02:59.180 --> 00:03:02.558 align:middle line:84% would make enormous amounts of money. 00:03:02.558 --> 00:03:04.100 align:middle line:84% At some point, the government decided 00:03:04.100 --> 00:03:05.858 align:middle line:84% to shift and auction off the right 00:03:05.858 --> 00:03:07.400 align:middle line:84% to provide cellular telephone service 00:03:07.400 --> 00:03:11.150 align:middle line:84% or auction off the right to send TV signals over the air. 00:03:11.150 --> 00:03:13.800 align:middle line:84% Those auctions raised tens of billions of dollars. 00:03:13.800 --> 00:03:16.370 align:middle line:84% Therefore, people wanted to hire lots of auction theorists 00:03:16.370 --> 00:03:19.680 align:middle line:84% to work on the auctions and design the auctions for them. 00:03:19.680 --> 00:03:21.140 align:middle line:84% And they raised a lot of interest. 00:03:21.140 --> 00:03:25.190 align:middle line:84% More recently, the online advertising example, again, 00:03:25.190 --> 00:03:28.310 align:middle line:84% there's tremendously complex auctions 00:03:28.310 --> 00:03:30.330 align:middle line:84% that you can run to auction advertising, 00:03:30.330 --> 00:03:32.083 align:middle line:84% and it spurred a lot of interest. 00:03:32.083 --> 00:03:33.500 align:middle line:84% There's also been a big literature 00:03:33.500 --> 00:03:35.810 align:middle line:84% on structural estimation of auctions. 00:03:35.810 --> 00:03:42.560 align:middle line:84% And mostly Tobias is going to do that in Wednesday's lecture. 00:03:42.560 --> 00:03:45.020 align:middle line:84% So I'm going to start with what's 00:03:45.020 --> 00:03:48.260 align:middle line:84% not a great model for applications, 00:03:48.260 --> 00:03:50.720 align:middle line:84% but it's a great model for solving the model 00:03:50.720 --> 00:03:52.260 align:middle line:90% and getting insights from it. 00:03:52.260 --> 00:03:55.510 align:middle line:84% So it's a special case, but I will do a lot of my analysis 00:03:55.510 --> 00:03:57.840 align:middle line:84% in the independent private values model. 00:03:57.840 --> 00:04:02.720 align:middle line:84% So here we have bidders indexed by i equals 1 to n. 00:04:02.720 --> 00:04:05.930 align:middle line:90% There's one object to be sold. 00:04:05.930 --> 00:04:07.623 align:middle line:84% So you can think of this as people, 00:04:07.623 --> 00:04:10.040 align:middle line:84% they're at a charity fundraiser and they're auctioning off 00:04:10.040 --> 00:04:10.970 align:middle line:90% a bottle of wine. 00:04:10.970 --> 00:04:13.790 align:middle line:84% And whoever wins the auction is going to take the bottle of wine 00:04:13.790 --> 00:04:16.640 align:middle line:84% and drink it or something like that. 00:04:16.640 --> 00:04:21.647 align:middle line:84% Each bidder observes a signal si that relates to their value. 00:04:21.647 --> 00:04:23.480 align:middle line:84% We're going to assume that these signals are 00:04:23.480 --> 00:04:26.570 align:middle line:90% independent across bidders. 00:04:26.570 --> 00:04:29.390 align:middle line:84% The term private values means that I know 00:04:29.390 --> 00:04:30.980 align:middle line:90% what the good is worth to me. 00:04:30.980 --> 00:04:33.950 align:middle line:84% My value is a function only of my own signal, not of 00:04:33.950 --> 00:04:35.070 align:middle line:90% everybody else's signal. 00:04:35.070 --> 00:04:37.380 align:middle line:90% So I know I'm an expert in wine. 00:04:37.380 --> 00:04:38.270 align:middle line:90% I see the wine. 00:04:38.270 --> 00:04:38.985 align:middle line:90% I see the label. 00:04:38.985 --> 00:04:40.610 align:middle line:84% I just know how much I'm going to enjoy 00:04:40.610 --> 00:04:42.300 align:middle line:90% drinking that bottle of wine. 00:04:42.300 --> 00:04:47.240 align:middle line:84% So my value depends only on my own signal. 00:04:47.240 --> 00:04:49.468 align:middle line:84% Once you make the decision that-- 00:04:49.468 --> 00:04:52.010 align:middle line:84% once you have the private values model, where your value only 00:04:52.010 --> 00:04:55.340 align:middle line:84% depends on your own signal, it's without loss of generality 00:04:55.340 --> 00:04:57.800 align:middle line:90% to say the signal is your value. 00:04:57.800 --> 00:04:59.870 align:middle line:84% So that's what we're going to typically do 00:04:59.870 --> 00:05:02.843 align:middle line:84% is everyone just observes their own value. 00:05:02.843 --> 00:05:05.010 align:middle line:84% We're going to assume that bidders are risk neutral. 00:05:05.010 --> 00:05:06.890 align:middle line:84% That is, you get a value of s minus p 00:05:06.890 --> 00:05:09.140 align:middle line:84% if you win the auction at a price of p. 00:05:09.140 --> 00:05:11.540 align:middle line:84% If you were to lose and be forced to pay p, 00:05:11.540 --> 00:05:13.250 align:middle line:84% either as an entry fee or something else, 00:05:13.250 --> 00:05:15.470 align:middle line:84% then your utility would be negative p. 00:05:15.470 --> 00:05:18.170 align:middle line:84% And the bidders are only going to observe their signal. 00:05:18.170 --> 00:05:21.390 align:middle line:84% This is also a model that people use for procurement auctions. 00:05:21.390 --> 00:05:25.310 align:middle line:84% If you think about it, you have a government 00:05:25.310 --> 00:05:29.220 align:middle line:84% is inviting contractors to bid on repaving Memorial Drive. 00:05:29.220 --> 00:05:32.390 align:middle line:84% You can think of the s as the amount of money 00:05:32.390 --> 00:05:36.295 align:middle line:84% that it will cost the firm to do the paving job. 00:05:36.295 --> 00:05:39.090 align:middle line:90% 00:05:39.090 --> 00:05:42.270 align:middle line:84% And s is obviously a big negative number. 00:05:42.270 --> 00:05:45.580 align:middle line:84% If you're asked to pave a road, it will cost you $2.7 million. 00:05:45.580 --> 00:05:48.880 align:middle line:84% So the s is therefore negative $2.7 million. 00:05:48.880 --> 00:05:51.588 align:middle line:84% And then what you're bidding is you're bidding a price. 00:05:51.588 --> 00:05:53.880 align:middle line:84% The price is going to be negative, like the price could 00:05:53.880 --> 00:05:55.560 align:middle line:90% be negative $3 million. 00:05:55.560 --> 00:06:00.990 align:middle line:84% And so if the price of getting the contract is negative $3 00:06:00.990 --> 00:06:03.090 align:middle line:84% million, your cost is negative $2.7 million, 00:06:03.090 --> 00:06:09.160 align:middle line:90% you get $300,000 in profits. 00:06:09.160 --> 00:06:12.470 align:middle line:84% First auction that's considered always by theorists, 00:06:12.470 --> 00:06:14.770 align:middle line:84% not so often used in practice, is the second price 00:06:14.770 --> 00:06:16.240 align:middle line:90% sealed bid auction. 00:06:16.240 --> 00:06:19.060 align:middle line:84% In the second price sealed bid auction, what you would do 00:06:19.060 --> 00:06:20.740 align:middle line:84% is you'd have every contractor say, 00:06:20.740 --> 00:06:22.790 align:middle line:84% I will pave the road for $2.5 million. 00:06:22.790 --> 00:06:24.560 align:middle line:90% I will pave the road for $2.7. 00:06:24.560 --> 00:06:25.760 align:middle line:90% I would do it for $2.8. 00:06:25.760 --> 00:06:28.730 align:middle line:84% Everyone just puts their bid in an envelope, seals it. 00:06:28.730 --> 00:06:29.990 align:middle line:90% They're all handed in. 00:06:29.990 --> 00:06:31.690 align:middle line:84% And then on the day of the auction, 00:06:31.690 --> 00:06:33.530 align:middle line:90% all the envelopes are opened. 00:06:33.530 --> 00:06:37.432 align:middle line:84% Whoever has bid, well, in the bidding 00:06:37.432 --> 00:06:39.640 align:middle line:84% for a positive price, whoever bids the highest amount 00:06:39.640 --> 00:06:40.880 align:middle line:90% is going to win. 00:06:40.880 --> 00:06:42.670 align:middle line:84% But instead of paying what they bid, 00:06:42.670 --> 00:06:45.010 align:middle line:90% they pay the second highest bid. 00:06:45.010 --> 00:06:47.590 align:middle line:84% So if the we're bidding for a painting 00:06:47.590 --> 00:06:55.390 align:middle line:84% and the bids are $2.4 million, $2.3 million, $2.2 million, 00:06:55.390 --> 00:06:57.160 align:middle line:90% you open the envelopes. 00:06:57.160 --> 00:06:59.620 align:middle line:84% This person gets the good, but they only 00:06:59.620 --> 00:07:04.660 align:middle line:84% pay the second highest bid instead of paying what they bid. 00:07:04.660 --> 00:07:05.570 align:middle line:90% Why do we do that? 00:07:05.570 --> 00:07:09.110 align:middle line:84% It turns out it becomes a very easy auction to analyze. 00:07:09.110 --> 00:07:11.920 align:middle line:84% And so it's a very nice mechanism in that sense. 00:07:11.920 --> 00:07:15.700 align:middle line:84% Proposition: in the second price sealed bid auction, 00:07:15.700 --> 00:07:19.370 align:middle line:84% it's a weakly dominant strategy to bid your true value. 00:07:19.370 --> 00:07:21.040 align:middle line:84% So you don't have to think strategically 00:07:21.040 --> 00:07:22.270 align:middle line:84% about what other people are bidding, 00:07:22.270 --> 00:07:23.728 align:middle line:90% what's the good worth to them. 00:07:23.728 --> 00:07:25.270 align:middle line:84% You just have this dominant strategy, 00:07:25.270 --> 00:07:30.280 align:middle line:84% which is just to write down your own value, bid that, and that's 00:07:30.280 --> 00:07:35.020 align:middle line:90% a dominant strategy equilibrium. 00:07:35.020 --> 00:07:36.490 align:middle line:84% A good way to think about that is 00:07:36.490 --> 00:07:38.990 align:middle line:84% to just think about what are the deviations you could do? 00:07:38.990 --> 00:07:42.610 align:middle line:90% So suppose your value is si. 00:07:42.610 --> 00:07:44.290 align:middle line:84% You consider writing down something 00:07:44.290 --> 00:07:47.710 align:middle line:84% that's different from your value and let b hat 00:07:47.710 --> 00:07:52.180 align:middle line:84% be the largest value written down by everybody else. 00:07:52.180 --> 00:07:57.110 align:middle line:84% There's six possible orderings of bs and b hat. 00:07:57.110 --> 00:07:59.810 align:middle line:84% In the middle cases here, I have the cases where-- sorry, 00:07:59.810 --> 00:08:01.880 align:middle line:84% in the first top and bottom cases. 00:08:01.880 --> 00:08:04.575 align:middle line:84% In the top and bottom cases, when somebody else 00:08:04.575 --> 00:08:06.200 align:middle line:84% has written down a number that's bigger 00:08:06.200 --> 00:08:09.200 align:middle line:84% than both your value and the number you wrote down, 00:08:09.200 --> 00:08:12.740 align:middle line:84% well then you lose whether you wrote down si or wrote down bi, 00:08:12.740 --> 00:08:14.990 align:middle line:84% and so your value is 0 either way. 00:08:14.990 --> 00:08:19.197 align:middle line:84% The other case is if everyone else bid lower numbers, 00:08:19.197 --> 00:08:21.530 align:middle line:84% things that are lower both than your value and the thing 00:08:21.530 --> 00:08:23.300 align:middle line:84% you wrote down, in this case, you're 00:08:23.300 --> 00:08:26.060 align:middle line:84% going to win the auction whether you wrote down bi or si 00:08:26.060 --> 00:08:27.867 align:middle line:84% and you're going to pay b hat either way. 00:08:27.867 --> 00:08:29.450 align:middle line:84% So the fact that you've done something 00:08:29.450 --> 00:08:32.630 align:middle line:84% different from writing down si also doesn't make a difference. 00:08:32.630 --> 00:08:35.059 align:middle line:84% The two cases we're writing something different from si 00:08:35.059 --> 00:08:38.690 align:middle line:84% does make a difference is here and here. 00:08:38.690 --> 00:08:40.487 align:middle line:90% Suppose that your value is si. 00:08:40.487 --> 00:08:43.070 align:middle line:84% Someone else wrote down a number that's bigger than your value 00:08:43.070 --> 00:08:45.018 align:middle line:84% and you write down something even bigger. 00:08:45.018 --> 00:08:47.060 align:middle line:84% Well then if you've written down your true value, 00:08:47.060 --> 00:08:48.650 align:middle line:90% you would have lost. 00:08:48.650 --> 00:08:51.740 align:middle line:84% Now that you win, you get the object 00:08:51.740 --> 00:08:54.260 align:middle line:84% and you pay b hat, which is more than it's worth to you. 00:08:54.260 --> 00:08:56.120 align:middle line:84% So you end up regretting that you 00:08:56.120 --> 00:08:59.500 align:middle line:84% won, because you've bid something more than it's worth. 00:08:59.500 --> 00:09:04.080 align:middle line:84% And then the final case is I would have won if I'd bid si, 00:09:04.080 --> 00:09:06.700 align:middle line:84% but I write something lower, and then I lose. 00:09:06.700 --> 00:09:09.510 align:middle line:84% And so here, instead of getting utility si minus b hat, 00:09:09.510 --> 00:09:11.140 align:middle line:90% I get utility 0. 00:09:11.140 --> 00:09:14.460 align:middle line:84% So in all six cases, I'm weakly worse off and in two of them 00:09:14.460 --> 00:09:16.150 align:middle line:90% I'm strictly worse off. 00:09:16.150 --> 00:09:20.833 align:middle line:84% So just writing down my true value is an optimal strategy. 00:09:20.833 --> 00:09:23.550 align:middle line:90% 00:09:23.550 --> 00:09:26.400 align:middle line:90% It's not the unique equilibrium. 00:09:26.400 --> 00:09:29.230 align:middle line:84% For instance, you could have one person bid in this model. 00:09:29.230 --> 00:09:32.340 align:middle line:84% One person bids s upper bar and everybody else bids 0. 00:09:32.340 --> 00:09:33.930 align:middle line:84% And then all the bidders bidding 0 00:09:33.930 --> 00:09:35.613 align:middle line:84% are happy to bid 0, because they can't 00:09:35.613 --> 00:09:37.530 align:middle line:84% win unless they bid s upper bar, which is more 00:09:37.530 --> 00:09:38.890 align:middle line:90% than it's worth to them. 00:09:38.890 --> 00:09:41.348 align:middle line:84% The person bidding s upper bar is happy to bid s upper bar, 00:09:41.348 --> 00:09:43.380 align:middle line:84% because he's going to get it at a price of 0. 00:09:43.380 --> 00:09:45.820 align:middle line:84% Usually we don't pay attention to those equilibria. 00:09:45.820 --> 00:09:48.990 align:middle line:84% So usually we think about this equilibrium of this game 00:09:48.990 --> 00:09:51.880 align:middle line:84% where everyone just plays their dominant strategy. 00:09:51.880 --> 00:09:54.130 align:middle line:90% And that's what they do. 00:09:54.130 --> 00:09:58.140 align:middle line:84% It is the unique symmetric equilibrium 00:09:58.140 --> 00:10:01.880 align:middle line:84% if you have continuous distributions. 00:10:01.880 --> 00:10:05.090 align:middle line:84% So one thing that's nice about this dominant strategy 00:10:05.090 --> 00:10:07.910 align:middle line:84% is now it's easy to figure out how much revenue the seller 00:10:07.910 --> 00:10:09.470 align:middle line:90% makes from this auction. 00:10:09.470 --> 00:10:11.510 align:middle line:84% So the amount the seller makes, I'm 00:10:11.510 --> 00:10:16.520 align:middle line:84% going to write sn minus 1 colon n for the n minus first order 00:10:16.520 --> 00:10:19.110 align:middle line:84% statistic of n draws from this distribution. 00:10:19.110 --> 00:10:21.360 align:middle line:84% So this is the n minus first highest. 00:10:21.360 --> 00:10:24.260 align:middle line:84% So because whatever the bids are, 00:10:24.260 --> 00:10:30.920 align:middle line:84% you always get the second highest or n minus first lowest 00:10:30.920 --> 00:10:31.800 align:middle line:90% bid. 00:10:31.800 --> 00:10:34.130 align:middle line:84% We just need to compute the expected value 00:10:34.130 --> 00:10:37.510 align:middle line:84% of this second highest draw from the distribution. 00:10:37.510 --> 00:10:40.970 align:middle line:84% And a good way to think about that 00:10:40.970 --> 00:10:48.830 align:middle line:84% is, how is it going to be that the second highest 00:10:48.830 --> 00:10:52.190 align:middle line:90% bid is exactly $2.3 million? 00:10:52.190 --> 00:10:55.520 align:middle line:84% The way that's going to happen is, 00:10:55.520 --> 00:10:59.570 align:middle line:84% suppose we have one bidder like bidder number three 00:10:59.570 --> 00:11:03.350 align:middle line:84% who has a higher value than this, one bidder who 00:11:03.350 --> 00:11:06.720 align:middle line:84% bids exactly this or within dx of this, 00:11:06.720 --> 00:11:11.150 align:middle line:84% and then you have all the rest of the bidders down here. 00:11:11.150 --> 00:11:12.650 align:middle line:84% There are many ways this can happen. 00:11:12.650 --> 00:11:14.000 align:middle line:84% It doesn't have to be bidder three up here 00:11:14.000 --> 00:11:14.790 align:middle line:90% and bidder seven here. 00:11:14.790 --> 00:11:16.580 align:middle line:84% It could be bidder four here and bidder nine here. 00:11:16.580 --> 00:11:18.630 align:middle line:84% It could be bidder one here, bidder two here. 00:11:18.630 --> 00:11:21.950 align:middle line:84% But for this particular configuration, the probability 00:11:21.950 --> 00:11:24.560 align:middle line:84% that bidder three is above this point x 00:11:24.560 --> 00:11:28.820 align:middle line:90% is 1 minus capital f of x. 00:11:28.820 --> 00:11:31.850 align:middle line:84% The probability that bidder seven is in this tiny interval 00:11:31.850 --> 00:11:35.030 align:middle line:90% is f of x dx. 00:11:35.030 --> 00:11:37.347 align:middle line:84% Because it has to be an interval dx around this. 00:11:37.347 --> 00:11:39.680 align:middle line:84% And then the probability that all the rest of the people 00:11:39.680 --> 00:11:45.580 align:middle line:84% are here is f of x to the n minus 2. 00:11:45.580 --> 00:11:48.508 align:middle line:84% So the total probability of a configuration 00:11:48.508 --> 00:11:50.050 align:middle line:84% like this with the second highest bid 00:11:50.050 --> 00:11:56.800 align:middle line:84% is x is just n times n minus 1 times this times this times 00:11:56.800 --> 00:11:57.590 align:middle line:90% that. 00:11:57.590 --> 00:12:00.880 align:middle line:84% Because there are n people who could be the high bidder, 00:12:00.880 --> 00:12:03.740 align:middle line:84% n minus 1 who could then be the second highest bidder. 00:12:03.740 --> 00:12:08.830 align:middle line:84% So this thing here and n minus 1 capital f of x to the n 00:12:08.830 --> 00:12:11.650 align:middle line:84% minus 2 little f of x1 minus f of x dx, 00:12:11.650 --> 00:12:15.820 align:middle line:84% that's the density of the second highest value. 00:12:15.820 --> 00:12:18.400 align:middle line:84% And so the expected second highest value 00:12:18.400 --> 00:12:20.745 align:middle line:84% is just integrate x times that density. 00:12:20.745 --> 00:12:23.930 align:middle line:90% 00:12:23.930 --> 00:12:26.780 align:middle line:84% So just as an example here, I do this 00:12:26.780 --> 00:12:28.213 align:middle line:90% for the uniform distribution. 00:12:28.213 --> 00:12:29.630 align:middle line:84% And the uniform distribution, this 00:12:29.630 --> 00:12:33.800 align:middle line:84% says that an auction with n bidders raises n minus 1 over n 00:12:33.800 --> 00:12:36.590 align:middle line:90% plus 1 as revenue. 00:12:36.590 --> 00:12:39.140 align:middle line:84% So the revenue from a second price 00:12:39.140 --> 00:12:41.600 align:middle line:84% sealed bid auction goes to 1 as the number of bidders 00:12:41.600 --> 00:12:44.330 align:middle line:84% goes to infinity, because the second highest 00:12:44.330 --> 00:12:48.980 align:middle line:84% value is almost the first value, which is almost the top anyway. 00:12:48.980 --> 00:12:51.800 align:middle line:84% And this density calculation, it's 00:12:51.800 --> 00:12:55.730 align:middle line:84% an example of just how you compute a k-th order 00:12:55.730 --> 00:13:00.890 align:middle line:84% statistic, which is you have n minus 1 00:13:00.890 --> 00:13:07.380 align:middle line:84% choose k minus 1 possible groups of people who can be above x. 00:13:07.380 --> 00:13:10.350 align:middle line:90% Who can be, sorry, below x. 00:13:10.350 --> 00:13:12.960 align:middle line:84% f of x to the k minus 1 is then the probability 00:13:12.960 --> 00:13:15.100 align:middle line:84% that each of them has a value below x. 00:13:15.100 --> 00:13:17.370 align:middle line:84% 1 minus f of x to the n minus k is a probability 00:13:17.370 --> 00:13:19.050 align:middle line:90% that everybody else is above x. 00:13:19.050 --> 00:13:23.040 align:middle line:84% And then you have f of x dx is the probability 00:13:23.040 --> 00:13:24.740 align:middle line:84% that someone has a value exactly x. 00:13:24.740 --> 00:13:27.930 align:middle line:90% 00:13:27.930 --> 00:13:32.310 align:middle line:84% And so computing expected values of auctions. 00:13:32.310 --> 00:13:35.710 align:middle line:84% Revenues, you're often computing these order statistics. 00:13:35.710 --> 00:13:38.820 align:middle line:84% And when the draws are independent and people bid 00:13:38.820 --> 00:13:43.200 align:middle line:84% truthfully, that's a fairly easy calculation to do. 00:13:43.200 --> 00:13:45.300 align:middle line:90% A second auction that's-- 00:13:45.300 --> 00:13:51.170 align:middle line:84% second price sealed bid auctions are this nice economic gain, 00:13:51.170 --> 00:13:53.860 align:middle line:84% nice model, because they're very simple. 00:13:53.860 --> 00:13:57.350 align:middle line:84% In practice, we don't see auctions conducted that way. 00:13:57.350 --> 00:13:59.440 align:middle line:84% In practice, what you often see is 00:13:59.440 --> 00:14:02.200 align:middle line:84% auctions conducted with an oral ascending bid process 00:14:02.200 --> 00:14:03.203 align:middle line:90% where you-- 00:14:03.203 --> 00:14:04.870 align:middle line:84% anyway, you probably haven't been there, 00:14:04.870 --> 00:14:09.472 align:middle line:84% but you watch people do auctions on TV for paintings 00:14:09.472 --> 00:14:10.930 align:middle line:84% and it's always people with paddles 00:14:10.930 --> 00:14:14.293 align:middle line:84% up in the air who will bid $1 million, $1.1, do I hear $1.2? 00:14:14.293 --> 00:14:16.210 align:middle line:84% People just keep raising their hand every time 00:14:16.210 --> 00:14:17.380 align:middle line:90% they want to bid higher. 00:14:17.380 --> 00:14:21.580 align:middle line:84% And then they keep bidding higher until the guy says, 00:14:21.580 --> 00:14:24.670 align:middle line:84% going, going, gone, because no one else is willing to bid more 00:14:24.670 --> 00:14:26.860 align:middle line:90% than the current bid amount. 00:14:26.860 --> 00:14:28.722 align:middle line:84% Analyzing that kind of game where 00:14:28.722 --> 00:14:31.180 align:middle line:84% people keep raising their hand would be a very complicated, 00:14:31.180 --> 00:14:32.510 align:middle line:90% extensive form. 00:14:32.510 --> 00:14:35.590 align:middle line:84% So what people do instead is simplify to this what's 00:14:35.590 --> 00:14:37.360 align:middle line:84% called the button auction design, which 00:14:37.360 --> 00:14:40.900 align:middle line:84% is the clock is going up and the auctioneer 00:14:40.900 --> 00:14:42.760 align:middle line:84% keeps calling out higher and higher numbers. 00:14:42.760 --> 00:14:45.460 align:middle line:84% And you just hold your finger on the button 00:14:45.460 --> 00:14:48.577 align:middle line:84% as long as you still want to buy the good at that price. 00:14:48.577 --> 00:14:50.660 align:middle line:84% And then once you take your finger off the button, 00:14:50.660 --> 00:14:52.770 align:middle line:84% you're out of the bidding and you've dropped out forever. 00:14:52.770 --> 00:14:54.540 align:middle line:84% So it's like, who's in, who's in, who's in. 00:14:54.540 --> 00:14:56.123 align:middle line:84% And then you just take your finger off 00:14:56.123 --> 00:14:57.500 align:middle line:90% and you're out permanently. 00:14:57.500 --> 00:14:59.450 align:middle line:84% That's nice, because it converts it 00:14:59.450 --> 00:15:01.730 align:middle line:84% to a basic one dimensional strategy 00:15:01.730 --> 00:15:04.760 align:middle line:84% space, which is I just choose at what point do I drop out 00:15:04.760 --> 00:15:05.440 align:middle line:90% of the auction? 00:15:05.440 --> 00:15:09.370 align:middle line:90% 00:15:09.370 --> 00:15:11.440 align:middle line:84% Thinking about that game of at what point 00:15:11.440 --> 00:15:13.640 align:middle line:84% or if I was giving instructions to a computer, 00:15:13.640 --> 00:15:16.930 align:middle line:84% at what point should you drop out of the bidding? 00:15:16.930 --> 00:15:18.820 align:middle line:84% It's clear that in some sense, this game 00:15:18.820 --> 00:15:21.400 align:middle line:84% is the second price sealed bid auction, just 00:15:21.400 --> 00:15:22.700 align:middle line:90% in a different form. 00:15:22.700 --> 00:15:24.790 align:middle line:84% So a perfect Bayesian equilibrium 00:15:24.790 --> 00:15:26.440 align:middle line:84% of this button auction model is just 00:15:26.440 --> 00:15:31.750 align:middle line:84% everybody drops out when the auctioneer gets 00:15:31.750 --> 00:15:32.810 align:middle line:90% to their true value. 00:15:32.810 --> 00:15:37.180 align:middle line:84% So as long as he's saying if the good is worth $2.4 million 00:15:37.180 --> 00:15:39.962 align:middle line:84% to you, as long as he's saying $2 million, $2.1, $2.3, 00:15:39.962 --> 00:15:41.420 align:middle line:84% you keep your finger on the button. 00:15:41.420 --> 00:15:44.087 align:middle line:84% And as soon as he gets $2.4, you take your finger off the button 00:15:44.087 --> 00:15:45.680 align:middle line:84% and say, I don't want it anymore. 00:15:45.680 --> 00:15:51.400 align:middle line:90% 00:15:51.400 --> 00:15:52.638 align:middle line:90% Why is this true? 00:15:52.638 --> 00:15:54.430 align:middle line:84% I think this one is actually it's even more 00:15:54.430 --> 00:15:57.280 align:middle line:84% obvious than the second price sealed bid auction. 00:15:57.280 --> 00:15:58.610 align:middle line:90% What's my dominant strategy? 00:15:58.610 --> 00:16:02.150 align:middle line:84% As long as I want to win, I keep saying I'm in. 00:16:02.150 --> 00:16:04.510 align:middle line:84% As soon as I don't want to pay what's being charged, 00:16:04.510 --> 00:16:06.370 align:middle line:90% I drop out. 00:16:06.370 --> 00:16:09.050 align:middle line:84% So it's the same argument as a second price sealed bid auction. 00:16:09.050 --> 00:16:11.985 align:middle line:84% Dropping out earlier could only make 00:16:11.985 --> 00:16:14.110 align:middle line:84% me lose something that I would want to have bought. 00:16:14.110 --> 00:16:17.500 align:middle line:84% And bidding past my value, all I can do 00:16:17.500 --> 00:16:20.870 align:middle line:84% is lose and end up paying more than I wanted to get for it. 00:16:20.870 --> 00:16:25.160 align:middle line:90% So the game is still the same. 00:16:25.160 --> 00:16:26.955 align:middle line:90% We get the second highest price. 00:16:26.955 --> 00:16:30.990 align:middle line:90% 00:16:30.990 --> 00:16:33.480 align:middle line:84% In practice, what's funny is if you 00:16:33.480 --> 00:16:37.710 align:middle line:84% run second price sealed bid auction models, 00:16:37.710 --> 00:16:39.780 align:middle line:90% people often get it wrong. 00:16:39.780 --> 00:16:41.550 align:middle line:84% People understand that I won't actually-- 00:16:41.550 --> 00:16:44.710 align:middle line:84% people understand I won't actually need to pay what I bid. 00:16:44.710 --> 00:16:46.780 align:middle line:84% I'll probably have to pay something less. 00:16:46.780 --> 00:16:49.110 align:middle line:84% They don't do that full consideration of the six cases 00:16:49.110 --> 00:16:51.820 align:middle line:84% and say, OK, I should still bid exactly what it's worth. 00:16:51.820 --> 00:16:54.820 align:middle line:84% And you will see in second price experiments, people over bid 00:16:54.820 --> 00:16:56.320 align:middle line:84% in second price sealed bid auctions. 00:16:56.320 --> 00:16:58.352 align:middle line:84% They realize, OK, I'm probably not going 00:16:58.352 --> 00:17:00.060 align:middle line:84% to have to pay what I bid, so therefore I 00:17:00.060 --> 00:17:02.160 align:middle line:84% can bid more than it's actually worth to me, 00:17:02.160 --> 00:17:03.780 align:middle line:84% and I probably won't have to pay that. 00:17:03.780 --> 00:17:08.910 align:middle line:84% Somehow the conditioning logic doesn't make it through. 00:17:08.910 --> 00:17:13.319 align:middle line:84% But in practice, I would say in practice people 00:17:13.319 --> 00:17:16.760 align:middle line:90% will tend to do first price-- 00:17:16.760 --> 00:17:18.470 align:middle line:84% will tend to do auctions of this variety 00:17:18.470 --> 00:17:20.470 align:middle line:84% rather than the second price sealed bid auction. 00:17:20.470 --> 00:17:22.490 align:middle line:84% One thing that is different about the auction 00:17:22.490 --> 00:17:23.990 align:middle line:84% from the auctioneer's perspective 00:17:23.990 --> 00:17:28.190 align:middle line:84% is the information that's revealed about the bids. 00:17:28.190 --> 00:17:31.400 align:middle line:84% In this auction, when you open the envelopes, 00:17:31.400 --> 00:17:34.160 align:middle line:84% you learn what the good was worth to everyone, 00:17:34.160 --> 00:17:37.010 align:middle line:84% and you may learn how much surplus 00:17:37.010 --> 00:17:39.260 align:middle line:84% went to the leading bidder, because the second highest 00:17:39.260 --> 00:17:42.380 align:middle line:84% bidder had a value much below the highest bidder. 00:17:42.380 --> 00:17:45.220 align:middle line:84% Whereas in this auction, you never learn. 00:17:45.220 --> 00:17:46.970 align:middle line:84% You learn when everybody else drops out. 00:17:46.970 --> 00:17:49.263 align:middle line:84% You never learn the value of the highest bidder. 00:17:49.263 --> 00:17:50.180 align:middle line:90% There were some cases. 00:17:50.180 --> 00:17:52.280 align:middle line:84% There was a famous spectrum auction 00:17:52.280 --> 00:17:54.020 align:middle line:84% case where they were auctioning off 00:17:54.020 --> 00:17:55.892 align:middle line:84% I think it was cellular telephone service, 00:17:55.892 --> 00:17:57.350 align:middle line:84% right to conduct cellular telephone 00:17:57.350 --> 00:18:00.140 align:middle line:84% service in some small town in New Zealand 00:18:00.140 --> 00:18:01.910 align:middle line:84% that basically only one person wanted 00:18:01.910 --> 00:18:03.470 align:middle line:90% to provide the service there. 00:18:03.470 --> 00:18:05.798 align:middle line:90% And I'll make up these numbers. 00:18:05.798 --> 00:18:06.840 align:middle line:90% They're completely wrong. 00:18:06.840 --> 00:18:11.450 align:middle line:84% But something like the high first person submitted $37 00:18:11.450 --> 00:18:14.760 align:middle line:84% million and the second one submitted $15,000 and then 00:18:14.760 --> 00:18:16.272 align:middle line:90% everyone else submitted 0. 00:18:16.272 --> 00:18:17.730 align:middle line:84% And then they open up the envelopes 00:18:17.730 --> 00:18:20.250 align:middle line:84% and they're like, OK, your brilliant auction design 00:18:20.250 --> 00:18:22.200 align:middle line:84% says we give it to the bidder number 00:18:22.200 --> 00:18:23.880 align:middle line:84% one, who is willing to pay $37 million. 00:18:23.880 --> 00:18:26.820 align:middle line:84% We charge them $15,000 and everyone's like, 00:18:26.820 --> 00:18:29.290 align:middle line:84% that was the worst auction design in history. 00:18:29.290 --> 00:18:31.150 align:middle line:84% How could you have recommended that? 00:18:31.150 --> 00:18:33.870 align:middle line:84% Obviously, if we'd done the oral ascending auction, 00:18:33.870 --> 00:18:37.530 align:middle line:84% all we would have seen is that only two people show up and one 00:18:37.530 --> 00:18:39.080 align:middle line:84% of them puts his hand down at 15,000. 00:18:39.080 --> 00:18:41.247 align:middle line:84% And we're like, OK, it's not worth providing service 00:18:41.247 --> 00:18:42.450 align:middle line:90% in this town. 00:18:42.450 --> 00:18:44.590 align:middle line:84% That was a reasonable price that we got. 00:18:44.590 --> 00:18:49.260 align:middle line:84% And so in practice that ex-post embarrassment of the auctioneer 00:18:49.260 --> 00:18:51.990 align:middle line:84% may be a factor that leads us not to do the second price 00:18:51.990 --> 00:18:53.126 align:middle line:90% sealed bid mechanism. 00:18:53.126 --> 00:19:01.670 align:middle line:90% 00:19:01.670 --> 00:19:06.350 align:middle line:84% Another mechanism that we see even more often in practice 00:19:06.350 --> 00:19:09.740 align:middle line:84% is the first price sealed bid mechanism. 00:19:09.740 --> 00:19:11.870 align:middle line:84% So the first price sealed bid mechanism 00:19:11.870 --> 00:19:13.910 align:middle line:84% would be like the second price sealed bid. 00:19:13.910 --> 00:19:16.050 align:middle line:84% You're running your procurement auction. 00:19:16.050 --> 00:19:19.400 align:middle line:84% You ask all the bidders to bid what price 00:19:19.400 --> 00:19:21.930 align:middle line:84% you would need to give them to get them to pave the road. 00:19:21.930 --> 00:19:23.720 align:middle line:90% They all submit their bids. 00:19:23.720 --> 00:19:28.550 align:middle line:84% And then the highest bidder wins and actually pays the bid. 00:19:28.550 --> 00:19:30.768 align:middle line:84% Or if we're buying something, I write down 00:19:30.768 --> 00:19:32.810 align:middle line:84% I'm willing to pay $2.4 million for the painting. 00:19:32.810 --> 00:19:35.310 align:middle line:84% Someone else writes down $2.3, $2.2. 00:19:35.310 --> 00:19:36.420 align:middle line:90% We open the envelopes. 00:19:36.420 --> 00:19:38.850 align:middle line:84% If I wrote down, I'm willing to pay $2.4 million, 00:19:38.850 --> 00:19:40.615 align:middle line:90% you charge me $2.4 million. 00:19:40.615 --> 00:19:43.600 align:middle line:90% 00:19:43.600 --> 00:19:45.730 align:middle line:84% What's the equilibrium of this game? 00:19:45.730 --> 00:19:48.590 align:middle line:84% Here this is a game where you have to shade your bids. 00:19:48.590 --> 00:19:50.980 align:middle line:84% You can't bid what the good is truly worth to you, 00:19:50.980 --> 00:19:54.250 align:middle line:84% because sometimes bidding what the good is worth to you 00:19:54.250 --> 00:19:57.280 align:middle line:90% is a weakly dominated strategy. 00:19:57.280 --> 00:20:00.100 align:middle line:84% If I'm willing to pay exactly $2.4 million, 00:20:00.100 --> 00:20:02.090 align:middle line:84% at any higher price, I wouldn't want it. 00:20:02.090 --> 00:20:06.830 align:middle line:84% If I bid $2.4 million, then if I lose, I get 0 utility. 00:20:06.830 --> 00:20:09.400 align:middle line:84% And if I win, I get 0 utility, because I've 00:20:09.400 --> 00:20:11.840 align:middle line:84% bid exactly everything that the good was worth to me. 00:20:11.840 --> 00:20:13.600 align:middle line:90% I get 0 surplus. 00:20:13.600 --> 00:20:14.620 align:middle line:90% So what do you do? 00:20:14.620 --> 00:20:18.400 align:middle line:84% It's like monopoly pricing where you shade your bid 00:20:18.400 --> 00:20:23.080 align:middle line:84% and you decide, I'm going to bid less than my true value. 00:20:23.080 --> 00:20:26.110 align:middle line:84% As I go further and further down below my true value, 00:20:26.110 --> 00:20:29.710 align:middle line:84% I get more profit if I am chosen as the winner, 00:20:29.710 --> 00:20:31.700 align:middle line:84% but it's less and less likely I'm going to win. 00:20:31.700 --> 00:20:33.370 align:middle line:84% So it's kind of like the monopolist 00:20:33.370 --> 00:20:34.760 align:middle line:90% raising price above cost. 00:20:34.760 --> 00:20:37.065 align:middle line:84% I get more and more profit if I do make the sale, 00:20:37.065 --> 00:20:39.190 align:middle line:84% but it's less and less likely that I make the sale. 00:20:39.190 --> 00:20:41.320 align:middle line:84% And you make that trade off of probability 00:20:41.320 --> 00:20:46.970 align:middle line:84% of winning times surplus versus surplus if I win. 00:20:46.970 --> 00:20:50.490 align:middle line:84% So let's think about what the equilibrium would look like. 00:20:50.490 --> 00:20:52.940 align:middle line:84% So suppose we had a symmetric equilibrium. 00:20:52.940 --> 00:20:55.950 align:middle line:84% Everyone's using these strictly increasing strategies. 00:20:55.950 --> 00:20:56.720 align:middle line:90% b star of s. 00:20:56.720 --> 00:21:01.880 align:middle line:84% The higher is my value or signal s, the higher I bid. 00:21:01.880 --> 00:21:03.150 align:middle line:90% My payoff. 00:21:03.150 --> 00:21:09.050 align:middle line:84% If I bid bi and everyone else uses b star is I get s minus bi 00:21:09.050 --> 00:21:10.620 align:middle line:90% is my prize. 00:21:10.620 --> 00:21:18.860 align:middle line:84% I get that prize if everybody else bids less than b star of sj 00:21:18.860 --> 00:21:20.660 align:middle line:90% is less than bi for all j. 00:21:20.660 --> 00:21:25.340 align:middle line:84% So I win if everybody else bids less than the amount that I bid. 00:21:25.340 --> 00:21:28.430 align:middle line:84% So that tells me that maximization problem 00:21:28.430 --> 00:21:30.050 align:middle line:84% would be that my optimal bid has to be 00:21:30.050 --> 00:21:37.880 align:middle line:84% the maximizer of si minus bi times f to the n minus 1. 00:21:37.880 --> 00:21:45.980 align:middle line:84% So the probability that b star of sj 00:21:45.980 --> 00:21:49.850 align:middle line:84% is less than or equal to bi is just the probability 00:21:49.850 --> 00:21:57.200 align:middle line:84% that sj is less than or equal to b star inverse of bi. 00:21:57.200 --> 00:21:59.690 align:middle line:84% So the probability that everybody else's signal 00:21:59.690 --> 00:22:07.880 align:middle line:84% is below b star inverse of bi is just f of b star inverse of bi 00:22:07.880 --> 00:22:11.764 align:middle line:90% raised to the n minus 1 power. 00:22:11.764 --> 00:22:15.200 align:middle line:84% And a trick for simplifying the analysis of this 00:22:15.200 --> 00:22:16.757 align:middle line:84% that you would think shouldn't work, 00:22:16.757 --> 00:22:19.340 align:middle line:84% but this is kind of like what we do in mechanism design often, 00:22:19.340 --> 00:22:23.690 align:middle line:84% is instead of thinking about people choosing their bid, 00:22:23.690 --> 00:22:29.680 align:middle line:84% think of people choosing pretending to be some other type 00:22:29.680 --> 00:22:33.220 align:middle line:84% and bidding like some other person with some other value 00:22:33.220 --> 00:22:35.380 align:middle line:90% bids in this. 00:22:35.380 --> 00:22:40.380 align:middle line:84% So if I'm thinking about what type s do I want to imitate? 00:22:40.380 --> 00:22:44.850 align:middle line:84% I'm then going to imitate type s by choosing b star of s. 00:22:44.850 --> 00:22:47.250 align:middle line:84% And then my value is going to be my price. 00:22:47.250 --> 00:22:48.420 align:middle line:90% I'm going to win s. 00:22:48.420 --> 00:22:51.450 align:middle line:84% I'm going to get a payoff of s minus b star of s 00:22:51.450 --> 00:22:53.770 align:middle line:84% if everyone else's value is less than s. 00:22:53.770 --> 00:22:56.250 align:middle line:84% So if I bid like the bidder who has type 00:22:56.250 --> 00:23:00.430 align:middle line:84% s, then I win whenever everybody else's type is less than s. 00:23:00.430 --> 00:23:02.790 align:middle line:84% And so I've eliminated this inverse function here, 00:23:02.790 --> 00:23:04.890 align:middle line:84% and I've got my payoff function I'm 00:23:04.890 --> 00:23:08.370 align:middle line:84% trying to maximize is s minus b star of s times 00:23:08.370 --> 00:23:11.900 align:middle line:90% f to the n minus 1 of s. 00:23:11.900 --> 00:23:13.580 align:middle line:84% So on the bottom line of that screen, 00:23:13.580 --> 00:23:15.350 align:middle line:84% I've taken the first order condition 00:23:15.350 --> 00:23:17.575 align:middle line:84% differentiating this with respect to s. 00:23:17.575 --> 00:23:20.310 align:middle line:90% 00:23:20.310 --> 00:23:22.200 align:middle line:84% Differentiating this with respect to s 00:23:22.200 --> 00:23:25.880 align:middle line:84% and setting it equal to 0 at s equals si. 00:23:25.880 --> 00:23:28.670 align:middle line:84% And so the derivative of this with respect to s 00:23:28.670 --> 00:23:33.530 align:middle line:84% is this term times the derivative of this one, which 00:23:33.530 --> 00:23:36.980 align:middle line:84% is n minus 1 f to the n minus 2 of si 00:23:36.980 --> 00:23:40.685 align:middle line:84% times little f of si and then plus this times 00:23:40.685 --> 00:23:42.560 align:middle line:84% the derivative of this, which is just minus b 00:23:42.560 --> 00:23:44.960 align:middle line:90% star prime evaluated at si. 00:23:44.960 --> 00:23:48.710 align:middle line:84% So that's the first order condition for my maximization 00:23:48.710 --> 00:23:51.290 align:middle line:84% when I'm thinking about which type do I want to copy 00:23:51.290 --> 00:23:55.170 align:middle line:84% and noting that the type I copy has to be me. 00:23:55.170 --> 00:23:59.770 align:middle line:84% So the trick here is that I know the equilibrium. 00:23:59.770 --> 00:24:04.200 align:middle line:84% I know the equilibrium is s star equals si. 00:24:04.200 --> 00:24:07.620 align:middle line:84% And so because you know the equilibrium is the identity, 00:24:07.620 --> 00:24:09.450 align:middle line:84% that simplifies what the expression 00:24:09.450 --> 00:24:14.450 align:middle line:84% is for the first order condition evaluated at the equilibrium. 00:24:14.450 --> 00:24:15.980 align:middle line:84% And now in the next three slides, 00:24:15.980 --> 00:24:19.105 align:middle line:84% I'm going to do three different rewritings of this. 00:24:19.105 --> 00:24:21.980 align:middle line:90% 00:24:21.980 --> 00:24:25.720 align:middle line:84% One rewriting I'm going to do is just. 00:24:25.720 --> 00:24:28.690 align:middle line:84% Think of myself as solving this for the bid. 00:24:28.690 --> 00:24:31.960 align:middle line:84% So I'm going to solve this equation for b star, 00:24:31.960 --> 00:24:34.750 align:middle line:84% and I'm going to do that by just taking this expression b 00:24:34.750 --> 00:24:38.980 align:middle line:84% star and n minus 1 f to the n minus 2 little f, 00:24:38.980 --> 00:24:43.210 align:middle line:84% move it to the other side, and then divide by this 00:24:43.210 --> 00:24:45.050 align:middle line:90% and see what's left. 00:24:45.050 --> 00:24:48.430 align:middle line:84% And what you get is the optimal bid 00:24:48.430 --> 00:24:53.410 align:middle line:84% is your true value minus a markdown. 00:24:53.410 --> 00:24:59.800 align:middle line:84% So this is an expression for how much you shade your bid. 00:24:59.800 --> 00:25:02.410 align:middle line:84% If I look at the numerator, you'll 00:25:02.410 --> 00:25:04.840 align:middle line:84% see that the numerator of this f to the n minus 1 00:25:04.840 --> 00:25:07.330 align:middle line:84% of si, that's just the probability 00:25:07.330 --> 00:25:10.942 align:middle line:84% that everyone else bids less than I bid. 00:25:10.942 --> 00:25:13.150 align:middle line:84% Because that's the probability that everyone else has 00:25:13.150 --> 00:25:15.460 align:middle line:90% a lower type than I do. 00:25:15.460 --> 00:25:18.340 align:middle line:84% So this is the probability that everyone else 00:25:18.340 --> 00:25:22.330 align:middle line:84% bids less than what I'm bidding in equilibrium. 00:25:22.330 --> 00:25:25.390 align:middle line:84% And then the denominator is just the derivative 00:25:25.390 --> 00:25:27.920 align:middle line:84% of the numerator with a change of variables formula. 00:25:27.920 --> 00:25:31.580 align:middle line:84% So you differentiate this g with respect to this. 00:25:31.580 --> 00:25:32.863 align:middle line:90% This is what you get. 00:25:32.863 --> 00:25:35.530 align:middle line:84% And then you have 1 over b star prime from a change of variables 00:25:35.530 --> 00:25:36.500 align:middle line:90% formula. 00:25:36.500 --> 00:25:42.400 align:middle line:84% So what we get is that what you do in a second price 00:25:42.400 --> 00:25:45.140 align:middle line:84% sealed bid auction is you mark down your bid. 00:25:45.140 --> 00:25:50.260 align:middle line:84% You mark it down by the ratio of the CDF of the bid distribution, 00:25:50.260 --> 00:25:53.890 align:middle line:84% the highest bid distribution evaluated at si, 00:25:53.890 --> 00:25:59.020 align:middle line:84% divided by the PDF of the highest bid distribution. 00:25:59.020 --> 00:26:02.300 align:middle line:84% So when do you shade your bids more? 00:26:02.300 --> 00:26:04.550 align:middle line:84% You're more aggressive in shading your bids 00:26:04.550 --> 00:26:07.270 align:middle line:84% if the probability of winning is higher 00:26:07.270 --> 00:26:11.860 align:middle line:84% and the density of the rival bid distribution is lower. 00:26:11.860 --> 00:26:15.730 align:middle line:84% Because this is kind of like an inverse elasticity 00:26:15.730 --> 00:26:17.470 align:middle line:90% rule for markups. 00:26:17.470 --> 00:26:22.900 align:middle line:84% The more bidders there who are bidding around almost exactly 00:26:22.900 --> 00:26:26.132 align:middle line:84% b star of si, the more you don't want to shade your bid, 00:26:26.132 --> 00:26:28.340 align:middle line:84% because if you shade your bid, you're likely to lose. 00:26:28.340 --> 00:26:31.630 align:middle line:84% But if this density is low, then every extra bit 00:26:31.630 --> 00:26:33.220 align:middle line:84% of shading you do has very little-- 00:26:33.220 --> 00:26:34.870 align:middle line:84% there's very little demand elasticity. 00:26:34.870 --> 00:26:37.287 align:middle line:84% There's very little impact on your probability of winning. 00:26:37.287 --> 00:26:39.140 align:middle line:84% So then you shade more aggressively. 00:26:39.140 --> 00:26:44.410 align:middle line:84% And so bid shading is based on how likely you are to win, 00:26:44.410 --> 00:26:46.210 align:middle line:84% which gives you the inframarginal gains 00:26:46.210 --> 00:26:48.170 align:middle line:90% from lowering the bid. 00:26:48.170 --> 00:26:51.740 align:middle line:84% And then the g is what's the increased probability of losing. 00:26:51.740 --> 00:26:57.040 align:middle line:84% And so I mark down based on those ratios. 00:26:57.040 --> 00:27:00.050 align:middle line:84% And this expression, I did it because Tobias is going 00:27:00.050 --> 00:27:01.310 align:middle line:90% to be lecturing on Wednesday. 00:27:01.310 --> 00:27:04.100 align:middle line:84% This is also a very, very big part 00:27:04.100 --> 00:27:06.410 align:middle line:84% of the structural estimation of auction models, 00:27:06.410 --> 00:27:12.240 align:middle line:84% because this is just the CDF of the rival bid distribution. 00:27:12.240 --> 00:27:14.160 align:middle line:84% This is the PDF of the rival bid distribution. 00:27:14.160 --> 00:27:16.170 align:middle line:90% These are estimable objects. 00:27:16.170 --> 00:27:18.890 align:middle line:84% That basic insight of structural estimation of auctions 00:27:18.890 --> 00:27:22.590 align:middle line:84% is this is observable, this is observable, this is observable. 00:27:22.590 --> 00:27:26.180 align:middle line:84% So that's how you can back out people's values. 00:27:26.180 --> 00:27:31.010 align:middle line:84% Anyway, Tobias will do that in much more detail on Wednesday. 00:27:31.010 --> 00:27:33.510 align:middle line:84% Second thing I'm going to do with that first order condition 00:27:33.510 --> 00:27:35.440 align:middle line:84% is I'm actually going to solve this auction. 00:27:35.440 --> 00:27:37.648 align:middle line:84% And again, this is something that it should not work, 00:27:37.648 --> 00:27:41.280 align:middle line:84% but the model is elegantly designed so that it does work. 00:27:41.280 --> 00:27:44.790 align:middle line:84% So this was our first order condition that 00:27:44.790 --> 00:27:47.320 align:middle line:90% determined the optimal bid. 00:27:47.320 --> 00:27:48.970 align:middle line:84% I'm going to rearrange it by putting 00:27:48.970 --> 00:27:51.320 align:middle line:84% all the things with negative signs on the left side. 00:27:51.320 --> 00:27:53.470 align:middle line:84% So I put the b star prime term on the left side, 00:27:53.470 --> 00:27:57.190 align:middle line:84% and I put this b star times this stuff on the left side. 00:27:57.190 --> 00:28:02.560 align:middle line:84% So I get b star of si times this order statistic 00:28:02.560 --> 00:28:09.220 align:middle line:84% plus b star prime times that CDF equals si times this density. 00:28:09.220 --> 00:28:12.430 align:middle line:84% And then you look at that expression and you're like, wow, 00:28:12.430 --> 00:28:15.610 align:middle line:84% I can integrate both sides of that. 00:28:15.610 --> 00:28:18.260 align:middle line:84% The left side is an exact derivative. 00:28:18.260 --> 00:28:19.910 align:middle line:84% It's a derivative of this expression, 00:28:19.910 --> 00:28:22.540 align:middle line:84% b star times f to the n minus 1, because this 00:28:22.540 --> 00:28:25.880 align:middle line:84% is b star times the derivative of f to the n minus 1 00:28:25.880 --> 00:28:28.660 align:middle line:84% and this is f of n minus 1 times b star prime. 00:28:28.660 --> 00:28:31.900 align:middle line:84% So b star times f to the n minus 1 00:28:31.900 --> 00:28:35.500 align:middle line:84% is the integral from s lower bar to si 00:28:35.500 --> 00:28:41.050 align:middle line:84% of this density on the right side. 00:28:41.050 --> 00:28:44.770 align:middle line:84% And then again, skipping steps, you 00:28:44.770 --> 00:28:48.020 align:middle line:84% can integrate this expression on the right side by parts. 00:28:48.020 --> 00:28:50.170 align:middle line:84% That's a trick someone found a while ago. 00:28:50.170 --> 00:28:52.390 align:middle line:84% And you can get a closed form for expression, 00:28:52.390 --> 00:28:56.560 align:middle line:84% which is your bid is your markup, your bid is 00:28:56.560 --> 00:29:00.100 align:middle line:84% your value minus this markdown, which is the integral from s 00:29:00.100 --> 00:29:04.240 align:middle line:84% bar to si f to the n minus 1 of x ex over capital f 00:29:04.240 --> 00:29:06.910 align:middle line:90% to the n minus 1 of s. 00:29:06.910 --> 00:29:12.383 align:middle line:84% So this first price sealed bid auction is solvable. 00:29:12.383 --> 00:29:13.800 align:middle line:84% The only thing you need to plug in 00:29:13.800 --> 00:29:16.270 align:middle line:84% is what is the distribution of the values. 00:29:16.270 --> 00:29:17.680 align:middle line:90% Is it a uniform distribution? 00:29:17.680 --> 00:29:19.630 align:middle line:84% Is it an exponential distribution? 00:29:19.630 --> 00:29:21.060 align:middle line:84% Any distribution for which you can 00:29:21.060 --> 00:29:23.700 align:middle line:84% do this integral of f to the n minus 1, 00:29:23.700 --> 00:29:25.950 align:middle line:84% you can just get a nice closed form solution 00:29:25.950 --> 00:29:28.680 align:middle line:90% for what an auction will be. 00:29:28.680 --> 00:29:34.350 align:middle line:84% For instance, down here, I did it for the uniform distribution. 00:29:34.350 --> 00:29:38.520 align:middle line:84% In the uniform distribution, f of x is just x. 00:29:38.520 --> 00:29:41.340 align:middle line:84% And so it's just the integral x to the n minus 1 dx. 00:29:41.340 --> 00:29:44.310 align:middle line:84% That integrates to x to the n over n. 00:29:44.310 --> 00:29:45.930 align:middle line:84% You evaluate that and this tells me 00:29:45.930 --> 00:29:48.690 align:middle line:84% that the optimal bid with uniform distributions 00:29:48.690 --> 00:29:52.080 align:middle line:84% is n minus 1 over n times your value. 00:29:52.080 --> 00:29:54.660 align:middle line:84% So as the number of bidders gets large, 00:29:54.660 --> 00:29:56.363 align:middle line:84% you're always shading your value. 00:29:56.363 --> 00:29:57.780 align:middle line:84% And with the uniform distribution, 00:29:57.780 --> 00:29:59.820 align:middle line:84% you're shading your value in a linear way. 00:29:59.820 --> 00:30:02.950 align:middle line:84% With n bidders, you just bid n minus 1 over n times your value. 00:30:02.950 --> 00:30:06.360 align:middle line:84% So if n is two, you bid half your value. n is 3, 00:30:06.360 --> 00:30:08.250 align:middle line:90% you bid 2/3 of your value. 00:30:08.250 --> 00:30:10.925 align:middle line:84% n is 10, you bid 90% of your value. 00:30:10.925 --> 00:30:13.690 align:middle line:90% 00:30:13.690 --> 00:30:18.290 align:middle line:84% But it's nothing special about the uniform distribution. 00:30:18.290 --> 00:30:20.970 align:middle line:84% You can solve this model however you do this. 00:30:20.970 --> 00:30:28.230 align:middle line:90% 00:30:28.230 --> 00:30:32.220 align:middle line:84% Another thing that you get from this 00:30:32.220 --> 00:30:35.250 align:middle line:84% is a proposition that helps you understand 00:30:35.250 --> 00:30:37.360 align:middle line:84% why the auction raised the revenue it does. 00:30:37.360 --> 00:30:40.710 align:middle line:84% The optimal bid expression I wrote down on the previous page 00:30:40.710 --> 00:30:44.160 align:middle line:84% is just I bid the expected second highest 00:30:44.160 --> 00:30:47.010 align:middle line:84% value conditional on having the highest value. 00:30:47.010 --> 00:30:48.850 align:middle line:90% So I know my signal. 00:30:48.850 --> 00:30:50.320 align:middle line:90% I do the thought experiment. 00:30:50.320 --> 00:30:53.130 align:middle line:84% If I did have the highest value, so everyone else's value 00:30:53.130 --> 00:30:57.370 align:middle line:84% was less than mine, what would be the second highest value? 00:30:57.370 --> 00:30:59.345 align:middle line:90% I bid the expectation of that. 00:30:59.345 --> 00:31:04.120 align:middle line:90% 00:31:04.120 --> 00:31:05.120 align:middle line:90% Why is that true? 00:31:05.120 --> 00:31:07.120 align:middle line:84% I don't have great intuition, but it's 00:31:07.120 --> 00:31:09.500 align:middle line:90% easy to see it mathematically. 00:31:09.500 --> 00:31:15.660 align:middle line:84% So in the previous slide, I had this expression for the-- 00:31:15.660 --> 00:31:16.500 align:middle line:90% I had this thing. 00:31:16.500 --> 00:31:18.490 align:middle line:84% I recognized both sides were derivatives, 00:31:18.490 --> 00:31:22.410 align:middle line:84% and I got this expression for b star of s as an integral. 00:31:22.410 --> 00:31:26.430 align:middle line:84% So that gives me b star of s is this integral 00:31:26.430 --> 00:31:30.180 align:middle line:84% of this density on the top and f to the n minus 1 on the bottom. 00:31:30.180 --> 00:31:32.490 align:middle line:84% But if you look at what this density is, 00:31:32.490 --> 00:31:36.270 align:middle line:84% n minus 1 f to the n minus 2 little f of x dx, 00:31:36.270 --> 00:31:40.110 align:middle line:84% that's the density of the highest of n minus 1 00:31:40.110 --> 00:31:42.660 align:middle line:90% draws from f. 00:31:42.660 --> 00:31:47.220 align:middle line:84% And so I'm integrating x times the density of the highest of n 00:31:47.220 --> 00:31:51.690 align:middle line:84% minus 1 draws from x from s lower bar up to capital 00:31:51.690 --> 00:31:55.270 align:middle line:84% s, and then I'm dividing by f to the n minus 1 of x. 00:31:55.270 --> 00:31:57.570 align:middle line:84% So when I divide by f to the n minus 1 of x, 00:31:57.570 --> 00:32:02.100 align:middle line:84% this is giving me this density conditional on the highest 00:32:02.100 --> 00:32:04.440 align:middle line:90% value being less than si. 00:32:04.440 --> 00:32:08.700 align:middle line:84% And so this is just the expected second highest bid 00:32:08.700 --> 00:32:11.360 align:middle line:84% conditional on the second highest bid being less than si. 00:32:11.360 --> 00:32:14.700 align:middle line:90% 00:32:14.700 --> 00:32:17.312 align:middle line:84% So third way to think about bidding. 00:32:17.312 --> 00:32:19.020 align:middle line:84% So thought about-- thinking about bidding 00:32:19.020 --> 00:32:20.020 align:middle line:90% in terms of markups. 00:32:20.020 --> 00:32:22.800 align:middle line:84% It turns out that a way to think about what the markups imply 00:32:22.800 --> 00:32:25.770 align:middle line:84% is that the way you bid is you just take your value, 00:32:25.770 --> 00:32:27.930 align:middle line:84% think about what the second highest value would be, 00:32:27.930 --> 00:32:31.150 align:middle line:90% and you bid that in expectation. 00:32:31.150 --> 00:32:33.480 align:middle line:84% So corollary of that observation is 00:32:33.480 --> 00:32:36.150 align:middle line:84% that first and second price auctions 00:32:36.150 --> 00:32:40.020 align:middle line:84% yield exactly the same expected revenue to the seller. 00:32:40.020 --> 00:32:42.540 align:middle line:84% The second price auction, clearly you're 00:32:42.540 --> 00:32:45.820 align:middle line:84% always getting the second highest value as your revenue. 00:32:45.820 --> 00:32:49.320 align:middle line:84% So it's just the expected second highest value is the revenue. 00:32:49.320 --> 00:32:52.980 align:middle line:84% In the first price sealed bid auction, what you're getting 00:32:52.980 --> 00:32:55.770 align:middle line:84% is the expectation over the-- you 00:32:55.770 --> 00:32:58.450 align:middle line:84% always sell it to the high value person. 00:32:58.450 --> 00:33:01.890 align:middle line:84% So I'm getting the expectation over the value of the high value 00:33:01.890 --> 00:33:06.270 align:middle line:84% person of the expected second, the expected highest of-- 00:33:06.270 --> 00:33:08.370 align:middle line:84% the expected second highest value 00:33:08.370 --> 00:33:10.530 align:middle line:84% conditional on the second highest value being less 00:33:10.530 --> 00:33:11.920 align:middle line:90% than that level. 00:33:11.920 --> 00:33:14.380 align:middle line:84% And so iterated expectation says that's just 00:33:14.380 --> 00:33:17.300 align:middle line:84% another way to compute the expected second highest value. 00:33:17.300 --> 00:33:19.098 align:middle line:84% I just condition on the highest value 00:33:19.098 --> 00:33:20.890 align:middle line:84% and say, what's the expected second highest 00:33:20.890 --> 00:33:23.390 align:middle line:84% value conditional on that being the highest value? 00:33:23.390 --> 00:33:26.260 align:middle line:84% And then I integrate out over all possible highest values. 00:33:26.260 --> 00:33:29.080 align:middle line:84% That is the expected second highest value. 00:33:29.080 --> 00:33:33.100 align:middle line:84% So because everyone's bidding expected second highest values 00:33:33.100 --> 00:33:36.310 align:middle line:84% conditional on winning, you get the same expected second highest 00:33:36.310 --> 00:33:38.990 align:middle line:90% value as the revenue. 00:33:38.990 --> 00:33:40.580 align:middle line:84% So this is a special case of what's 00:33:40.580 --> 00:33:42.747 align:middle line:84% called the revenue equivalence theorem that you have 00:33:42.747 --> 00:33:45.298 align:middle line:84% these seemingly different auction mechanisms, 00:33:45.298 --> 00:33:47.840 align:middle line:84% one where people bid truthfully, one where people shade bids, 00:33:47.840 --> 00:33:52.730 align:middle line:84% and somehow they raise exactly the same revenue. 00:33:52.730 --> 00:33:55.670 align:middle line:84% I would say this is actually one of the most misunderstood 00:33:55.670 --> 00:33:57.710 align:middle line:90% things. 00:33:57.710 --> 00:34:01.370 align:middle line:84% You talk to people who are doing selling auctions online, 00:34:01.370 --> 00:34:04.080 align:middle line:84% which are often sold through second price mechanisms. 00:34:04.080 --> 00:34:09.889 align:middle line:84% And just at every company that does this, many times per year, 00:34:09.889 --> 00:34:12.560 align:middle line:84% every year, some executive comes up and realizes, 00:34:12.560 --> 00:34:15.170 align:middle line:84% wait, people are bidding this and we're only charging them 00:34:15.170 --> 00:34:16.469 align:middle line:90% the second highest value. 00:34:16.469 --> 00:34:19.290 align:middle line:90% I can get this 1 over n thing. 00:34:19.290 --> 00:34:21.407 align:middle line:84% There's this big gap that's $42 million. 00:34:21.407 --> 00:34:23.449 align:middle line:84% We should switch to a first price auction instead 00:34:23.449 --> 00:34:24.647 align:middle line:90% of a second price auction. 00:34:24.647 --> 00:34:26.480 align:middle line:84% And obviously, the mistake in that reasoning 00:34:26.480 --> 00:34:30.920 align:middle line:84% is yes, if you had the same bids and you changed the rule, 00:34:30.920 --> 00:34:32.130 align:middle line:90% you would get more money. 00:34:32.130 --> 00:34:34.031 align:middle line:84% But when you change the rules, people 00:34:34.031 --> 00:34:35.489 align:middle line:84% will just start shading their bids. 00:34:35.489 --> 00:34:36.510 align:middle line:90% They will bid less. 00:34:36.510 --> 00:34:40.190 align:middle line:84% You'll raise exactly the same revenue 00:34:40.190 --> 00:34:42.147 align:middle line:84% with the first or second price mechanism. 00:34:42.147 --> 00:34:43.730 align:middle line:84% We often think second price mechanisms 00:34:43.730 --> 00:34:45.688 align:middle line:84% are better because in second rights mechanisms, 00:34:45.688 --> 00:34:48.110 align:middle line:84% people can think about how much to bid, which is just 00:34:48.110 --> 00:34:50.810 align:middle line:84% what's it worth to me, whereas in the first price mechanism, 00:34:50.810 --> 00:34:53.719 align:middle line:84% they have to do this complicated reasoning about bid shading 00:34:53.719 --> 00:34:56.300 align:middle line:84% and what would be the expected second highest bid given what 00:34:56.300 --> 00:34:57.260 align:middle line:90% I know. 00:34:57.260 --> 00:34:59.090 align:middle line:84% It's putting all that work on the firms 00:34:59.090 --> 00:35:00.430 align:middle line:90% is not doing you any good. 00:35:00.430 --> 00:35:04.580 align:middle line:90% 00:35:04.580 --> 00:35:08.512 align:middle line:84% Anyway, revenue equivalence theorem-- 00:35:08.512 --> 00:35:10.220 align:middle line:84% and I'm going to go through this quickly. 00:35:10.220 --> 00:35:13.410 align:middle line:84% Consider more general auction mechanism. 00:35:13.410 --> 00:35:15.050 align:middle line:90% Imagine you had any game. 00:35:15.050 --> 00:35:18.200 align:middle line:84% The bidders just submit bids b1 through bn. 00:35:18.200 --> 00:35:21.390 align:middle line:84% The good is allocated to bidders with some probability 00:35:21.390 --> 00:35:23.240 align:middle line:84% that depends on what all the bids are. 00:35:23.240 --> 00:35:25.490 align:middle line:84% And the payments are some function 00:35:25.490 --> 00:35:26.670 align:middle line:90% of what all the bids are. 00:35:26.670 --> 00:35:29.513 align:middle line:84% So the first price sealed bid auction would fit this. 00:35:29.513 --> 00:35:32.180 align:middle line:84% You give it with probability 1, the person with the highest bid, 00:35:32.180 --> 00:35:33.720 align:middle line:90% and they paid their bid. 00:35:33.720 --> 00:35:35.887 align:middle line:84% The second price auction is, again, 00:35:35.887 --> 00:35:37.970 align:middle line:84% you give it to the person who had the highest bid, 00:35:37.970 --> 00:35:40.990 align:middle line:84% but they pay the second highest of these numbers. 00:35:40.990 --> 00:35:45.190 align:middle line:84% But it's a general class of auction mechanisms. 00:35:45.190 --> 00:35:48.480 align:middle line:84% Theorem is consider the symmetric independent private 00:35:48.480 --> 00:35:49.890 align:middle line:90% values model. 00:35:49.890 --> 00:35:53.370 align:middle line:84% Suppose that a general auction mechanism has an equilibrium 00:35:53.370 --> 00:35:56.820 align:middle line:84% bidding function in which the object is awarded 00:35:56.820 --> 00:36:00.060 align:middle line:84% to the bidder with the highest value and a bidder with value 00:36:00.060 --> 00:36:03.400 align:middle line:90% s lower bar gets 0 surplus. 00:36:03.400 --> 00:36:06.690 align:middle line:84% Then in equilibrium, the seller's expected revenue 00:36:06.690 --> 00:36:08.310 align:middle line:84% is the same thing we've just seen, 00:36:08.310 --> 00:36:10.660 align:middle line:84% the expected second highest value. 00:36:10.660 --> 00:36:14.220 align:middle line:84% And not only are the auctions equivalent in terms of revenue, 00:36:14.220 --> 00:36:16.290 align:middle line:84% they're equivalent from the bidder perspective 00:36:16.290 --> 00:36:20.520 align:middle line:84% in that the expected utility of a bidder who has type si 00:36:20.520 --> 00:36:22.590 align:middle line:84% is just the integral from s lower 00:36:22.590 --> 00:36:25.865 align:middle line:84% bar to si f to the n minus 1 of x dx. 00:36:25.865 --> 00:36:27.990 align:middle line:84% You'll hear people refer to this as the information 00:36:27.990 --> 00:36:29.260 align:middle line:90% rent of the bidder. 00:36:29.260 --> 00:36:33.330 align:middle line:84% But in any mechanism you choose that has these two 00:36:33.330 --> 00:36:37.320 align:middle line:84% natural properties, you always raise the same revenue, 00:36:37.320 --> 00:36:39.930 align:middle line:84% and you raise the same revenue because you always 00:36:39.930 --> 00:36:43.830 align:middle line:84% maximize gross surplus and you give away this much surplus 00:36:43.830 --> 00:36:45.510 align:middle line:90% to a bidder of type si. 00:36:45.510 --> 00:36:48.270 align:middle line:84% So they're strongly equivalent in that they 00:36:48.270 --> 00:36:50.160 align:middle line:84% raise the same revenue for the seller 00:36:50.160 --> 00:36:52.410 align:middle line:84% and they give the same expected utility 00:36:52.410 --> 00:36:55.170 align:middle line:84% for a buyer and expected utility, 00:36:55.170 --> 00:36:57.830 align:middle line:84% even conditional on knowing your type, it's always the same. 00:36:57.830 --> 00:37:01.820 align:middle line:90% 00:37:01.820 --> 00:37:05.180 align:middle line:84% And the thing I gave earlier on first and second price auctions 00:37:05.180 --> 00:37:06.350 align:middle line:90% is a special case of this. 00:37:06.350 --> 00:37:08.570 align:middle line:84% Because a first and second price auction games, 00:37:08.570 --> 00:37:11.600 align:middle line:84% I gave you the option, the object 00:37:11.600 --> 00:37:13.760 align:middle line:84% was always being awarded in equilibrium 00:37:13.760 --> 00:37:15.632 align:middle line:84% to the bidder with the highest value, 00:37:15.632 --> 00:37:17.090 align:middle line:84% whether in the second price auction 00:37:17.090 --> 00:37:20.300 align:middle line:84% because you stated your value or in the first price 00:37:20.300 --> 00:37:23.430 align:middle line:84% auction because you bid n minus 1 over n times your value. 00:37:23.430 --> 00:37:25.700 align:middle line:84% And then also a bidder with the lowest value 00:37:25.700 --> 00:37:28.460 align:middle line:84% was going to get 0 profits, because they 00:37:28.460 --> 00:37:30.440 align:middle line:90% win with probability 0. 00:37:30.440 --> 00:37:31.340 align:middle line:90% Yes. 00:37:31.340 --> 00:37:34.880 align:middle line:84% STUDENT: Isn't the second condition, more of a result? 00:37:34.880 --> 00:37:37.610 align:middle line:84% Because I thought the whole notion of the revenue 00:37:37.610 --> 00:37:39.585 align:middle line:84% equivalence theorem is you can set 00:37:39.585 --> 00:37:45.170 align:middle line:84% s lower bar's value to whatever you want and then it comes out. 00:37:45.170 --> 00:37:47.490 align:middle line:84% And then you argue, well, in this case, 00:37:47.490 --> 00:37:49.312 align:middle line:90% we just keep lowering it. 00:37:49.312 --> 00:37:51.020 align:middle line:84% GLENN ELLISON: Well, so I guess if you're 00:37:51.020 --> 00:37:52.520 align:middle line:90% thinking about optimal. 00:37:52.520 --> 00:37:53.930 align:middle line:84% If you're thinking about optimal, 00:37:53.930 --> 00:37:56.090 align:middle line:84% you could design mechanisms with the s lower bar 00:37:56.090 --> 00:37:58.520 align:middle line:90% type gets positive surplus. 00:37:58.520 --> 00:38:01.920 align:middle line:84% And then you wouldn't want to use-- those mechanisms would 00:38:01.920 --> 00:38:06.480 align:middle line:84% provide less revenue to the seller and more surplus 00:38:06.480 --> 00:38:07.390 align:middle line:90% to the buyer. 00:38:07.390 --> 00:38:10.920 align:middle line:84% So we tend to think of these as the mechanisms you 00:38:10.920 --> 00:38:12.670 align:middle line:84% would normally think someone would choose. 00:38:12.670 --> 00:38:14.420 align:middle line:84% And if you choose a mechanism to make sure 00:38:14.420 --> 00:38:16.890 align:middle line:84% the s lower bar type gets 0 surplus, 00:38:16.890 --> 00:38:19.380 align:middle line:84% then these things are going to hold. 00:38:19.380 --> 00:38:22.770 align:middle line:84% Yeah, there are worse mechanisms that give positive surplus, 00:38:22.770 --> 00:38:24.510 align:middle line:90% the s lower bar types. 00:38:24.510 --> 00:38:27.675 align:middle line:84% There are better mechanisms that give negative surplus to the s 00:38:27.675 --> 00:38:28.390 align:middle line:90% lower bar types. 00:38:28.390 --> 00:38:30.098 align:middle line:84% But then how do you get the s lower types 00:38:30.098 --> 00:38:32.280 align:middle line:90% to participate in them? 00:38:32.280 --> 00:38:35.220 align:middle line:84% So in some sense, this theorem says that-- 00:38:35.220 --> 00:38:37.140 align:middle line:84% and sometimes I really don't like it, 00:38:37.140 --> 00:38:39.690 align:middle line:84% because it makes you think the field of auction design 00:38:39.690 --> 00:38:41.190 align:middle line:84% is completely irrelevant, because it 00:38:41.190 --> 00:38:43.950 align:middle line:84% says that all auctions work out the same. 00:38:43.950 --> 00:38:46.180 align:middle line:90% And the reason why it's a-- 00:38:46.180 --> 00:38:46.680 align:middle line:90% let me see. 00:38:46.680 --> 00:38:49.680 align:middle line:90% So I have a proof here, again. 00:38:49.680 --> 00:38:52.110 align:middle line:84% Alex does a proof in [14.]124 if you want to see one. 00:38:52.110 --> 00:38:55.272 align:middle line:90% There's a proof. 00:38:55.272 --> 00:38:56.730 align:middle line:84% Actually, before I get to comments, 00:38:56.730 --> 00:38:59.190 align:middle line:84% let me just do one application of the revenue 00:38:59.190 --> 00:39:01.500 align:middle line:90% equivalence theorem. 00:39:01.500 --> 00:39:03.060 align:middle line:84% Revenue equivalence theorem can also 00:39:03.060 --> 00:39:06.820 align:middle line:90% be a tool for solving auctions. 00:39:06.820 --> 00:39:09.450 align:middle line:84% So here's an example, an all pay auction. 00:39:09.450 --> 00:39:13.990 align:middle line:84% In the all pay auction, bidders submit bids b1 through bn. 00:39:13.990 --> 00:39:16.170 align:middle line:84% The high value bidder is awarded the object, 00:39:16.170 --> 00:39:19.990 align:middle line:84% but everyone pays what they bid, win or lose. 00:39:19.990 --> 00:39:22.830 align:middle line:84% So in this case, it's kind of like buying lottery tickets 00:39:22.830 --> 00:39:25.320 align:middle line:90% or raffle tickets. 00:39:25.320 --> 00:39:27.460 align:middle line:90% We just all submit our bids. 00:39:27.460 --> 00:39:30.370 align:middle line:84% Everyone actually has to pay their bid, win or lose. 00:39:30.370 --> 00:39:32.750 align:middle line:84% And then whoever bid the highest amount gets the object. 00:39:32.750 --> 00:39:36.080 align:middle line:90% 00:39:36.080 --> 00:39:40.310 align:middle line:84% You can think of it as there are examples like lobbying. 00:39:40.310 --> 00:39:45.230 align:middle line:84% Imagine you're trying to win the rights to hold the next world 00:39:45.230 --> 00:39:46.390 align:middle line:90% cup in Qatar. 00:39:46.390 --> 00:39:49.110 align:middle line:90% 00:39:49.110 --> 00:39:52.040 align:middle line:84% Every country who wants a world cup submits bribes to FIFA. 00:39:52.040 --> 00:39:54.600 align:middle line:84% Whoever submits the highest bribe is going to win. 00:39:54.600 --> 00:39:56.450 align:middle line:84% If you submit the second highest bribe, 00:39:56.450 --> 00:39:58.070 align:middle line:90% you don't get your bribe back. 00:39:58.070 --> 00:40:02.510 align:middle line:84% You've given the millions of dollars to whatever person. 00:40:02.510 --> 00:40:06.650 align:middle line:84% We all pay our bribes and then the highest bribe wins. 00:40:06.650 --> 00:40:08.720 align:middle line:84% This, again, would be an auction that the revenue 00:40:08.720 --> 00:40:10.940 align:middle line:84% equivalence theorem would apply to. 00:40:10.940 --> 00:40:14.720 align:middle line:84% And so because the revenue equivalence theorem applies, 00:40:14.720 --> 00:40:20.520 align:middle line:84% we know that a bidder of type si gets this much surplus. 00:40:20.520 --> 00:40:24.750 align:middle line:84% Integral of s lower bar to s f to the n minus 1 of x dx. 00:40:24.750 --> 00:40:27.910 align:middle line:84% But in this all pay auction, it's 00:40:27.910 --> 00:40:30.310 align:middle line:84% also an easy expression for your expected utility. 00:40:30.310 --> 00:40:31.810 align:middle line:84% Your expected utility in equilibrium 00:40:31.810 --> 00:40:34.210 align:middle line:84% is just your value times the probability 00:40:34.210 --> 00:40:37.670 align:middle line:84% that wealth has a lower value minus what you bid. 00:40:37.670 --> 00:40:40.360 align:middle line:84% So if this minus this equals this, 00:40:40.360 --> 00:40:42.410 align:middle line:84% we get a markdown rule for your bid. 00:40:42.410 --> 00:40:45.580 align:middle line:84% Your bid is the expected surplus you're 00:40:45.580 --> 00:40:47.140 align:middle line:84% going to get from winning when you 00:40:47.140 --> 00:40:52.780 align:middle line:84% have the highest value minus your information rent. 00:40:52.780 --> 00:40:55.600 align:middle line:84% And so the revenue equivalence theorem, once you know it, 00:40:55.600 --> 00:40:57.970 align:middle line:84% can be a tool for actually computing 00:40:57.970 --> 00:41:00.670 align:middle line:84% equilibria of other auctions, because you 00:41:00.670 --> 00:41:02.860 align:middle line:84% know that the equilibrium must be such that people 00:41:02.860 --> 00:41:04.940 align:middle line:90% get exactly that surplus. 00:41:04.940 --> 00:41:06.680 align:middle line:84% And sometimes you can figure out. 00:41:06.680 --> 00:41:08.320 align:middle line:84% This case, you can figure out what 00:41:08.320 --> 00:41:11.080 align:middle line:84% the bids must be for everyone to get that surplus. 00:41:11.080 --> 00:41:14.950 align:middle line:84% So anyway, it's a beautiful theorem. 00:41:14.950 --> 00:41:17.890 align:middle line:84% In practice, it's really not a good-- 00:41:17.890 --> 00:41:20.488 align:middle line:84% it has that basic thing to think about. 00:41:20.488 --> 00:41:22.030 align:middle line:84% We have to think about people bidding 00:41:22.030 --> 00:41:24.550 align:middle line:90% strategically and markdowns. 00:41:24.550 --> 00:41:28.850 align:middle line:84% There is an enormous field of auction design despite this. 00:41:28.850 --> 00:41:32.290 align:middle line:84% And that's because the revenue equivalence theorem really 00:41:32.290 --> 00:41:34.263 align:middle line:84% doesn't cover the interesting cases. 00:41:34.263 --> 00:41:37.680 align:middle line:90% 00:41:37.680 --> 00:41:42.660 align:middle line:84% Many of the assumptions in revenue equivalence theorem 00:41:42.660 --> 00:41:45.420 align:middle line:84% are just not going to hold in practice. 00:41:45.420 --> 00:41:48.360 align:middle line:84% One is the bidders are assumed to be risk neutral. 00:41:48.360 --> 00:41:52.295 align:middle line:84% If you're talking about bidders bidding on paving contracts, 00:41:52.295 --> 00:41:53.670 align:middle line:84% they have businesses to run, they 00:41:53.670 --> 00:41:55.770 align:middle line:84% have employees who are going to be idle, 00:41:55.770 --> 00:41:57.040 align:middle line:90% it's not a long run thing. 00:41:57.040 --> 00:42:00.810 align:middle line:84% They can't be completely risk neutral. 00:42:00.810 --> 00:42:04.020 align:middle line:84% Third one, values are independent. 00:42:04.020 --> 00:42:05.610 align:middle line:84% Even if I was having a hard time, 00:42:05.610 --> 00:42:07.027 align:middle line:84% I always have a hard time thinking 00:42:07.027 --> 00:42:09.400 align:middle line:84% of cases where the signals are actually 00:42:09.400 --> 00:42:10.630 align:middle line:90% going to be independent. 00:42:10.630 --> 00:42:14.410 align:middle line:84% So it could be that I actually know exactly how much I 00:42:14.410 --> 00:42:15.570 align:middle line:90% like this bottle of wine. 00:42:15.570 --> 00:42:16.970 align:middle line:90% I just have a valuation for it. 00:42:16.970 --> 00:42:19.345 align:middle line:84% I'm bidding for this value of wine against somebody else. 00:42:19.345 --> 00:42:21.310 align:middle line:84% But in practice, if somebody else 00:42:21.310 --> 00:42:23.530 align:middle line:84% looked at that bottle of wine and they like it a lot, 00:42:23.530 --> 00:42:25.822 align:middle line:84% it's probably they know something about how good it is. 00:42:25.822 --> 00:42:27.750 align:middle line:84% If the wine actually tastes good, 00:42:27.750 --> 00:42:29.500 align:middle line:84% their signal is going to tell me something 00:42:29.500 --> 00:42:31.810 align:middle line:84% about how much I'm going to enjoy that bottle of wine. 00:42:31.810 --> 00:42:34.430 align:middle line:84% If it's a painting I intend to hang on my wall, 00:42:34.430 --> 00:42:36.345 align:middle line:84% I know how much I like the painting. 00:42:36.345 --> 00:42:37.720 align:middle line:84% But the fact that someone else is 00:42:37.720 --> 00:42:38.890 align:middle line:84% willing to pay a lot for the painting, 00:42:38.890 --> 00:42:41.098 align:middle line:84% I always have the option of selling it to them later. 00:42:41.098 --> 00:42:43.640 align:middle line:84% So if there are a lot of other people who like this painting, 00:42:43.640 --> 00:42:45.370 align:middle line:84% then that painting is more valuable to me 00:42:45.370 --> 00:42:49.360 align:middle line:84% because of the option value of selling it. 00:42:49.360 --> 00:42:52.630 align:middle line:84% Many, many cases, if I know that other-- 00:42:52.630 --> 00:42:56.300 align:middle line:84% if this is a good object, we're all going to it a lot. 00:42:56.300 --> 00:42:58.580 align:middle line:84% If this is a bad object, we're not going to it a lot. 00:42:58.580 --> 00:43:02.080 align:middle line:84% And so both the values are independent 00:43:02.080 --> 00:43:04.270 align:middle line:84% and the values only depend on my signal 00:43:04.270 --> 00:43:06.970 align:middle line:84% rather than on other people's signals as well. 00:43:06.970 --> 00:43:10.910 align:middle line:84% Those two things just don't seem realistic for many applications, 00:43:10.910 --> 00:43:13.730 align:middle line:84% because the fact that other people value something 00:43:13.730 --> 00:43:16.250 align:middle line:84% tells you something inherent about the object itself 00:43:16.250 --> 00:43:19.500 align:middle line:84% that then tells you something about my value. 00:43:19.500 --> 00:43:21.930 align:middle line:84% Or even just that I like it means 00:43:21.930 --> 00:43:24.700 align:middle line:84% that this is a bottle of wine that I unusually like. 00:43:24.700 --> 00:43:27.960 align:middle line:84% Someone else probably has the same tastes. 00:43:27.960 --> 00:43:32.070 align:middle line:84% And then the second limitation is the set of mechanisms 00:43:32.070 --> 00:43:33.330 align:middle line:90% that it considers. 00:43:33.330 --> 00:43:36.390 align:middle line:84% It only considers mechanisms where you always 00:43:36.390 --> 00:43:39.070 align:middle line:84% allocate the good to the high value bidder. 00:43:39.070 --> 00:43:41.440 align:middle line:84% It doesn't let you not allocate the good. 00:43:41.440 --> 00:43:45.570 align:middle line:84% So just some examples of things people in IO 00:43:45.570 --> 00:43:48.400 align:middle line:84% have noted about how you would bid differently. 00:43:48.400 --> 00:43:50.590 align:middle line:84% So suppose bidders are risk averse. 00:43:50.590 --> 00:43:54.810 align:middle line:84% They get utility u of s minus p if they win and u of minus p 00:43:54.810 --> 00:43:55.510 align:middle line:90% if they lose. 00:43:55.510 --> 00:43:58.830 align:middle line:84% So this is our small construction company 00:43:58.830 --> 00:44:05.100 align:middle line:84% that cares about its revenues in a nonlinear way. 00:44:05.100 --> 00:44:08.430 align:middle line:84% In this game, revenue equivalence theorem 00:44:08.430 --> 00:44:10.560 align:middle line:84% doesn't hold anymore and the first price auction 00:44:10.560 --> 00:44:14.660 align:middle line:84% raises more revenue than a second price auction. 00:44:14.660 --> 00:44:15.840 align:middle line:90% Why would that be? 00:44:15.840 --> 00:44:18.110 align:middle line:84% Imagine you're in a first price auction 00:44:18.110 --> 00:44:21.110 align:middle line:84% and compare the equilibrium of the first price auction 00:44:21.110 --> 00:44:22.970 align:middle line:84% where you bid n minus 1 over n times v 00:44:22.970 --> 00:44:24.845 align:middle line:84% to the equivalent of the second price auction 00:44:24.845 --> 00:44:28.760 align:middle line:84% where you bid v. Those two auctions 00:44:28.760 --> 00:44:31.730 align:middle line:84% have exactly the same expected surplus 00:44:31.730 --> 00:44:34.950 align:middle line:90% in dollars to the bidder. 00:44:34.950 --> 00:44:37.310 align:middle line:84% That was the revenue equivalence theorem said. 00:44:37.310 --> 00:44:42.620 align:middle line:84% But if in a first price auction, I raise my bid a little bit, 00:44:42.620 --> 00:44:46.270 align:middle line:84% I'm increasing the probability that I win, 00:44:46.270 --> 00:44:48.460 align:middle line:84% which is reducing the probability of the bad state 00:44:48.460 --> 00:44:51.220 align:middle line:84% where I get 0, and it's lowering my surplus 00:44:51.220 --> 00:44:52.970 align:middle line:84% in the good states where I do win. 00:44:52.970 --> 00:44:55.730 align:middle line:84% So what it's doing is it's to first order, 00:44:55.730 --> 00:44:57.820 align:middle line:84% it's not changing your expected payment 00:44:57.820 --> 00:44:59.380 align:middle line:84% by the revenue equivalence theorem, 00:44:59.380 --> 00:45:01.420 align:middle line:84% but it's reducing the variance in your payment 00:45:01.420 --> 00:45:04.660 align:middle line:84% by increasing the probability of winning a small amount instead 00:45:04.660 --> 00:45:06.980 align:middle line:84% of a lower probability of winning a bigger amount. 00:45:06.980 --> 00:45:09.430 align:middle line:84% And so in the first price sealed bid auction, 00:45:09.430 --> 00:45:13.150 align:middle line:84% if everyone else was bidding b star of si, 00:45:13.150 --> 00:45:16.370 align:middle line:84% you would raise your bid in the first price sealed bid auction. 00:45:16.370 --> 00:45:19.430 align:middle line:84% Second price sealed bid auction is unchanged. 00:45:19.430 --> 00:45:21.880 align:middle line:84% You always still have the same dominant strategy. 00:45:21.880 --> 00:45:24.730 align:middle line:84% So with risk averse bidders, first price auctions 00:45:24.730 --> 00:45:28.240 align:middle line:84% raise more revenue than second price auctions. 00:45:28.240 --> 00:45:30.670 align:middle line:84% Second example is if you have auctions 00:45:30.670 --> 00:45:34.510 align:middle line:84% with positively correlated values in auctions where 00:45:34.510 --> 00:45:37.180 align:middle line:84% the bidder's values are positively correlated, 00:45:37.180 --> 00:45:39.340 align:middle line:84% second price auctions raise more expected revenue 00:45:39.340 --> 00:45:40.750 align:middle line:90% than first price auctions. 00:45:40.750 --> 00:45:43.655 align:middle line:84% And there is a big literature on auction design 00:45:43.655 --> 00:45:46.280 align:middle line:84% and a big set of people who are professional auction designers, 00:45:46.280 --> 00:45:50.270 align:middle line:84% because to the extent that every auction differs 00:45:50.270 --> 00:45:54.470 align:middle line:84% from independent private values in some direction, 00:45:54.470 --> 00:45:57.260 align:middle line:84% you're going to think about all of these results that have been 00:45:57.260 --> 00:45:59.510 align:middle line:84% shown about when first and second or all pay 00:45:59.510 --> 00:46:02.450 align:middle line:84% auctions do better and pick out an auction that works well 00:46:02.450 --> 00:46:04.910 align:middle line:90% in that circumstance. 00:46:04.910 --> 00:46:08.450 align:middle line:84% A second stark example of what this revenue equivalent 00:46:08.450 --> 00:46:12.020 align:middle line:84% theorem doesn't do is think about the case 00:46:12.020 --> 00:46:13.940 align:middle line:90% where there's n equals 1. 00:46:13.940 --> 00:46:15.470 align:middle line:90% There's one bidder. 00:46:15.470 --> 00:46:20.840 align:middle line:84% That bidder has a value that's uniformly distributed on 0, 1. 00:46:20.840 --> 00:46:24.290 align:middle line:84% This is the classic monopoly pricing problem 00:46:24.290 --> 00:46:27.535 align:middle line:84% that I started in lecture one with. 00:46:27.535 --> 00:46:29.660 align:middle line:84% What does the revenue equivalence theorem consider? 00:46:29.660 --> 00:46:32.727 align:middle line:84% It considers mechanisms that always sell the good well. 00:46:32.727 --> 00:46:34.310 align:middle line:84% So if you have to always sell the good 00:46:34.310 --> 00:46:37.110 align:middle line:84% and the bidder has a value v that's drawn uniform 0, 1, 00:46:37.110 --> 00:46:38.985 align:middle line:84% the only mechanism that always sells the good 00:46:38.985 --> 00:46:40.300 align:middle line:90% is to sell it for a price of 0. 00:46:40.300 --> 00:46:42.800 align:middle line:84% And I started this class with a thing to do in this model is 00:46:42.800 --> 00:46:45.140 align:middle line:84% to set a price of 1/2 rather than a price of 0, 00:46:45.140 --> 00:46:48.470 align:middle line:84% because that maximizes probability of selling times 00:46:48.470 --> 00:46:50.010 align:middle line:90% value if you do sell. 00:46:50.010 --> 00:46:53.360 align:middle line:84% But if you have to sell with probability 1, all you can do 00:46:53.360 --> 00:46:55.370 align:middle line:84% is give the object away for free. 00:46:55.370 --> 00:46:59.120 align:middle line:84% So revenue equivalence theorem mechanisms 00:46:59.120 --> 00:47:04.210 align:middle line:84% always give the object away for free to the s lower bar type. 00:47:04.210 --> 00:47:08.320 align:middle line:84% So you can charge s lower bar, but they always give away 00:47:08.320 --> 00:47:10.660 align:middle line:84% the good with probability 1, which 00:47:10.660 --> 00:47:13.087 align:middle line:84% means you're always giving away that surplus that we were 00:47:13.087 --> 00:47:14.920 align:middle line:84% in monopoly pricing where I was telling you, 00:47:14.920 --> 00:47:16.830 align:middle line:90% you don't want to give away. 00:47:16.830 --> 00:47:20.940 align:middle line:84% So revenue equivalence theorem is considering a limited class 00:47:20.940 --> 00:47:23.460 align:middle line:84% of mechanisms which don't include the mechanisms you 00:47:23.460 --> 00:47:24.845 align:middle line:90% would actually want to use. 00:47:24.845 --> 00:47:28.490 align:middle line:90% 00:47:28.490 --> 00:47:33.200 align:middle line:84% So let me just think about reserve prices. 00:47:33.200 --> 00:47:36.320 align:middle line:84% What's your intuition for if we now go into an auction, 00:47:36.320 --> 00:47:38.370 align:middle line:84% do I want to set a reserve price in my auction 00:47:38.370 --> 00:47:40.620 align:middle line:84% or do I not want to set a reserve price in my auction? 00:47:40.620 --> 00:47:44.040 align:middle line:84% Or with one bidder, you know you need a reserve price. 00:47:44.040 --> 00:47:45.630 align:middle line:90% You want to set it equal to 1/2. 00:47:45.630 --> 00:47:47.810 align:middle line:90% What would I do with n bidders? 00:47:47.810 --> 00:47:52.100 align:middle line:84% Two intuitions you might have is that the more bidders there are, 00:47:52.100 --> 00:47:53.810 align:middle line:84% the less need there is to set a reserve 00:47:53.810 --> 00:47:58.310 align:middle line:84% price, because the competition is going to set the reserve 00:47:58.310 --> 00:48:00.260 align:middle line:90% equivalent for me. 00:48:00.260 --> 00:48:05.750 align:middle line:84% But then on the alternate side, the more bidders 00:48:05.750 --> 00:48:08.340 align:middle line:84% there are, the less chance that the reserve price is binding. 00:48:08.340 --> 00:48:10.882 align:middle line:84% So the downside of the reserve, they don't sell the good also 00:48:10.882 --> 00:48:12.200 align:middle line:90% goes away. 00:48:12.200 --> 00:48:16.700 align:middle line:84% So it turns out the theorem is in a second price sealed 00:48:16.700 --> 00:48:21.300 align:middle line:84% bid auction, you always set the monopoly price as the reserve. 00:48:21.300 --> 00:48:22.970 align:middle line:84% So what you want to do is, regardless 00:48:22.970 --> 00:48:25.310 align:middle line:84% of how many bidders there are, you just 00:48:25.310 --> 00:48:29.940 align:middle line:84% set a reserve price equal to the monopoly price. 00:48:29.940 --> 00:48:33.860 align:middle line:84% And I say that just before these bids are drawn, 00:48:33.860 --> 00:48:36.200 align:middle line:84% I just think ex-ante what would the monopoly 00:48:36.200 --> 00:48:38.540 align:middle line:90% price be to a single bidder? 00:48:38.540 --> 00:48:41.150 align:middle line:84% I announce in advance, this is the reserve. 00:48:41.150 --> 00:48:44.180 align:middle line:84% If you want the good, you must be at at least that reserve. 00:48:44.180 --> 00:48:46.370 align:middle line:84% You can't get the good unless you 00:48:46.370 --> 00:48:48.582 align:middle line:84% bid at least that reserve or the sale price 00:48:48.582 --> 00:48:50.040 align:middle line:84% will always be at least the reserve 00:48:50.040 --> 00:48:53.966 align:middle line:84% if you're the only one who bids above the reserve price. 00:48:53.966 --> 00:48:59.390 align:middle line:84% And simple reasoning for that is think about a relaxed problem 00:48:59.390 --> 00:49:02.840 align:middle line:84% where the seller actually gets to choose a reserve price not 00:49:02.840 --> 00:49:05.000 align:middle line:84% in advance before conducting the auction, 00:49:05.000 --> 00:49:07.940 align:middle line:84% but after observing where the second highest bidder dropped 00:49:07.940 --> 00:49:08.610 align:middle line:90% out. 00:49:08.610 --> 00:49:10.100 align:middle line:90% So you had n bidders. 00:49:10.100 --> 00:49:11.740 align:middle line:84% n minus 1 of them have dropped out. 00:49:11.740 --> 00:49:14.240 align:middle line:84% And suppose you can cheat and after the n minus first bidder 00:49:14.240 --> 00:49:15.360 align:middle line:90% has dropped out. 00:49:15.360 --> 00:49:18.080 align:middle line:84% so someone dropped out at 2.3 million. 00:49:18.080 --> 00:49:20.990 align:middle line:84% I now know that this guy is willing to pay at least 2.3 00:49:20.990 --> 00:49:21.570 align:middle line:90% million. 00:49:21.570 --> 00:49:25.250 align:middle line:84% And I think, what's the reserve price just for him? 00:49:25.250 --> 00:49:27.730 align:middle line:84% So it's a customized reserve price. 00:49:27.730 --> 00:49:36.030 align:middle line:84% Well, so I have these n draws from this distribution. 00:49:36.030 --> 00:49:39.090 align:middle line:84% I know that n minus 1 of the draws 00:49:39.090 --> 00:49:42.420 align:middle line:84% are down here below this value, this drop 00:49:42.420 --> 00:49:45.600 align:middle line:90% out point, sn minus 1 colon n. 00:49:45.600 --> 00:49:49.600 align:middle line:84% What's my posterior on the value of the remaining bidder? 00:49:49.600 --> 00:49:51.900 align:middle line:84% My posterior on the value of the remaining bidder 00:49:51.900 --> 00:49:54.840 align:middle line:84% is just that it's a single draw from the upper tail 00:49:54.840 --> 00:49:57.450 align:middle line:84% of the distribution I started from. 00:49:57.450 --> 00:50:05.460 align:middle line:84% So if I set a reserve price of r, which is bigger than this, 00:50:05.460 --> 00:50:08.190 align:middle line:84% the probability that I'm going to sell the good is just 1 00:50:08.190 --> 00:50:14.370 align:middle line:84% minus f of r over 1 minus f of sn minus 1 colon n. 00:50:14.370 --> 00:50:17.580 align:middle line:84% It's just a single draw from the distribution 00:50:17.580 --> 00:50:19.990 align:middle line:84% conditional on the value being at least this. 00:50:19.990 --> 00:50:22.350 align:middle line:90% And so this is the inverse CDF. 00:50:22.350 --> 00:50:26.430 align:middle line:84% This is the upper, upper tail CDF of that. 00:50:26.430 --> 00:50:31.810 align:middle line:84% So the expected profit that I'm going to get is just r times 1 00:50:31.810 --> 00:50:36.980 align:middle line:84% minus f of r divided by this, which is just the constant. 00:50:36.980 --> 00:50:40.610 align:middle line:84% So if you think about how do I maximize this expression 00:50:40.610 --> 00:50:44.000 align:middle line:84% r times 1 minus f of r times this constant, 00:50:44.000 --> 00:50:46.880 align:middle line:84% I just maximize that by maximizing 00:50:46.880 --> 00:50:49.970 align:middle line:84% r times 1 minus f of r, which is the monopoly pricing 00:50:49.970 --> 00:50:51.220 align:middle line:90% problem for one customer. 00:50:51.220 --> 00:50:57.300 align:middle line:90% 00:50:57.300 --> 00:51:01.590 align:middle line:84% So I have this monopoly profit when I use a price of r. 00:51:01.590 --> 00:51:03.740 align:middle line:90% Monopoly profits like this. 00:51:03.740 --> 00:51:09.690 align:middle line:84% If sn minus 1 colon n is here, if everyone else has dropped out 00:51:09.690 --> 00:51:13.590 align:middle line:84% low, I'm below the ex-ante monopoly price, 00:51:13.590 --> 00:51:16.290 align:middle line:84% then I would want to use the monopoly price as a reserve, 00:51:16.290 --> 00:51:18.840 align:middle line:84% because it's going to raise more revenue. 00:51:18.840 --> 00:51:22.950 align:middle line:84% Whereas if sn minus 1 colon n was up here, 00:51:22.950 --> 00:51:26.310 align:middle line:84% if everybody's bid really high, well above the monopoly price, 00:51:26.310 --> 00:51:29.160 align:middle line:84% then I don't want to use the reserve price anymore, 00:51:29.160 --> 00:51:30.990 align:middle line:84% because anything reserve price I do 00:51:30.990 --> 00:51:33.690 align:middle line:90% is just decreasing my revenue. 00:51:33.690 --> 00:51:37.830 align:middle line:84% But in either case, just setting this in the low case, 00:51:37.830 --> 00:51:39.690 align:middle line:84% this is the binding reserve you want. 00:51:39.690 --> 00:51:41.560 align:middle line:84% In the high case, you don't want to reserve. 00:51:41.560 --> 00:51:43.430 align:middle line:84% And this is a non-binding reserve. 00:51:43.430 --> 00:51:48.420 align:middle line:84% So ex-post, it's always optimal to set pm as the reserve. 00:51:48.420 --> 00:51:50.820 align:middle line:84% And so ex-ante, it's always optimal to set pm 00:51:50.820 --> 00:51:51.990 align:middle line:90% as the reserve. 00:51:51.990 --> 00:51:54.330 align:middle line:84% So what you do in a second price sealed bid auction 00:51:54.330 --> 00:51:58.180 align:middle line:84% is you monopoly price as a reserve, 00:51:58.180 --> 00:52:02.602 align:middle line:84% and then that is the fully optimal mechanism. 00:52:02.602 --> 00:52:04.810 align:middle line:84% So obviously if you're thinking about auction design, 00:52:04.810 --> 00:52:09.310 align:middle line:84% you need to think about what is that expected ex-ante monopoly 00:52:09.310 --> 00:52:14.620 align:middle line:84% price, because as the number of bidders goes up, 00:52:14.620 --> 00:52:17.260 align:middle line:84% the value of reserve prices do go down, 00:52:17.260 --> 00:52:20.120 align:middle line:84% because they're probably not going to be relevant anyway. 00:52:20.120 --> 00:52:23.370 align:middle line:84% But you still want the high reserve price. 00:52:23.370 --> 00:52:28.260 align:middle line:84% And competition doesn't mean don't use reserve prices. 00:52:28.260 --> 00:52:32.280 align:middle line:90% Some comments here. 00:52:32.280 --> 00:52:34.380 align:middle line:84% Reserve prices are positive even if the seller 00:52:34.380 --> 00:52:36.630 align:middle line:90% doesn't have any value. 00:52:36.630 --> 00:52:39.310 align:middle line:84% Reserve prices do reduce social welfare. 00:52:39.310 --> 00:52:41.970 align:middle line:84% So this is an inefficiency of auction mechanisms 00:52:41.970 --> 00:52:45.190 align:middle line:84% is you use reserve prices, they create deadweight loss. 00:52:45.190 --> 00:52:48.300 align:middle line:84% Now, they only create deadweight loss 00:52:48.300 --> 00:52:51.340 align:middle line:84% if all the bidders have values below the reserve price. 00:52:51.340 --> 00:52:56.970 align:middle line:84% So it's less of an issue, but it's still a social loss. 00:52:56.970 --> 00:52:59.250 align:middle line:84% The above analysis ignores entry. 00:52:59.250 --> 00:53:03.480 align:middle line:84% If you think about bidders like in the paving contract, paving 00:53:03.480 --> 00:53:05.750 align:middle line:84% Memorial Drive application, it's going 00:53:05.750 --> 00:53:08.250 align:middle line:84% to take bidders quite a long time to put together their bids 00:53:08.250 --> 00:53:10.042 align:middle line:84% and figure out exactly how much is it going 00:53:10.042 --> 00:53:11.320 align:middle line:90% to cost them to do the job. 00:53:11.320 --> 00:53:14.490 align:middle line:84% They're going to exert a lot of effort to submit a bid. 00:53:14.490 --> 00:53:16.950 align:middle line:84% If you put in a high reserve price, then 00:53:16.950 --> 00:53:19.087 align:middle line:84% they know that their surplus is going to be low. 00:53:19.087 --> 00:53:20.670 align:middle line:84% That's going to make you want to spend 00:53:20.670 --> 00:53:24.630 align:middle line:90% less time entering the auction. 00:53:24.630 --> 00:53:28.320 align:middle line:84% Entry costs can make reserve prices not as good of an idea 00:53:28.320 --> 00:53:31.470 align:middle line:84% as you think, because if you put in a high entry, 00:53:31.470 --> 00:53:34.050 align:middle line:84% if there's a high reserve price and therefore people 00:53:34.050 --> 00:53:38.130 align:middle line:84% don't enter the auction, then attracting fewer bidders 00:53:38.130 --> 00:53:39.250 align:middle line:90% is going to be a cost. 00:53:39.250 --> 00:53:42.000 align:middle line:84% There's a theorem in a Bulow Klemperer paper showing that 00:53:42.000 --> 00:53:44.760 align:middle line:84% even in ex-ante sense, if you attract one fewer 00:53:44.760 --> 00:53:49.230 align:middle line:84% bidder in expectation, then you're actually worse off 00:53:49.230 --> 00:53:52.110 align:middle line:84% from having used the optimal reserve price. 00:53:52.110 --> 00:53:54.300 align:middle line:84% And then another common reserve prices 00:53:54.300 --> 00:53:55.830 align:middle line:84% is there can be commitment problems 00:53:55.830 --> 00:53:57.250 align:middle line:90% in setting reserve price. 00:53:57.250 --> 00:54:00.718 align:middle line:84% We say we're only going to pay at most $2.1 million 00:54:00.718 --> 00:54:02.260 align:middle line:84% to repave Memorial Drive because it's 00:54:02.260 --> 00:54:04.070 align:middle line:90% got all these potholes in it. 00:54:04.070 --> 00:54:06.570 align:middle line:84% Everyone bids that it's going to take more than $2.1 million 00:54:06.570 --> 00:54:07.690 align:middle line:90% to do the work. 00:54:07.690 --> 00:54:09.240 align:middle line:90% What do you do then? 00:54:09.240 --> 00:54:11.160 align:middle line:84% Or if it's a bridge that's falling down, 00:54:11.160 --> 00:54:13.950 align:middle line:84% we're only going to pay $2.1 million to replace this bridge. 00:54:13.950 --> 00:54:17.020 align:middle line:84% If everyone else bids more than that, what do you do? 00:54:17.020 --> 00:54:20.010 align:middle line:84% Do you really commit, OK, I'm never going to fix that bridge 00:54:20.010 --> 00:54:22.010 align:middle line:90% or repave that road? 00:54:22.010 --> 00:54:23.760 align:middle line:84% You're going to want to then put in a bid, 00:54:23.760 --> 00:54:26.080 align:middle line:84% say, OK, I guess $2.1 million was too low. 00:54:26.080 --> 00:54:28.680 align:middle line:84% Now I'll have a reserve of $2.3 million. 00:54:28.680 --> 00:54:30.910 align:middle line:84% Reserve prices only work if you can commit to them. 00:54:30.910 --> 00:54:34.960 align:middle line:84% They don't work if you undo them later on. 00:54:34.960 --> 00:54:38.340 align:middle line:84% So then the final theory topic I'm going to do, 00:54:38.340 --> 00:54:42.523 align:middle line:84% I'll skip the next one after it, is common value auctions. 00:54:42.523 --> 00:54:45.680 align:middle line:90% 00:54:45.680 --> 00:54:47.780 align:middle line:84% More general model of auctions is 00:54:47.780 --> 00:54:52.250 align:middle line:84% that your value depends on your signal and everybody else's 00:54:52.250 --> 00:54:53.067 align:middle line:90% signal. 00:54:53.067 --> 00:54:54.650 align:middle line:84% So imagine you have these signals that 00:54:54.650 --> 00:54:58.220 align:middle line:84% have joint density f and your expected value 00:54:58.220 --> 00:55:02.450 align:middle line:84% depends on your signal and everybody else's signal. 00:55:02.450 --> 00:55:05.880 align:middle line:84% A special case of this is the pure common values model. 00:55:05.880 --> 00:55:09.380 align:middle line:84% So suppose the object has value v to all bidders. 00:55:09.380 --> 00:55:12.630 align:middle line:84% And we get signals which are v plus epsilon. 00:55:12.630 --> 00:55:15.320 align:middle line:84% So I'm going to talk about an empirical paper about oil 00:55:15.320 --> 00:55:16.125 align:middle line:90% drilling. 00:55:16.125 --> 00:55:17.750 align:middle line:84% So imagine you're bidding for the right 00:55:17.750 --> 00:55:21.890 align:middle line:84% to drill for oil on some tract of land offshore. 00:55:21.890 --> 00:55:25.310 align:middle line:84% The value of winning that auction is the amount of oil 00:55:25.310 --> 00:55:27.890 align:middle line:84% that you're going to get to extract from that well. 00:55:27.890 --> 00:55:31.580 align:middle line:84% And we all hire geologists and all of our geologists 00:55:31.580 --> 00:55:35.130 align:middle line:84% do sonic testing or whatever geologists do. 00:55:35.130 --> 00:55:37.520 align:middle line:84% And then they try to estimate what's the probability 00:55:37.520 --> 00:55:38.250 align:middle line:90% that there's oil. 00:55:38.250 --> 00:55:40.040 align:middle line:84% If there is oil, how much is there? 00:55:40.040 --> 00:55:41.940 align:middle line:84% And come up with an estimate of the value. 00:55:41.940 --> 00:55:46.770 align:middle line:84% And suppose they all get these values v plus epsilon i. 00:55:46.770 --> 00:55:49.080 align:middle line:84% The bidder's expected value given all signals 00:55:49.080 --> 00:55:52.380 align:middle line:84% is what's my expected value given my signal 00:55:52.380 --> 00:55:54.960 align:middle line:84% and what everybody else's geologists said. 00:55:54.960 --> 00:56:00.760 align:middle line:84% But I only observe my own signal. 00:56:00.760 --> 00:56:02.620 align:middle line:84% So imagine we have this pure common values 00:56:02.620 --> 00:56:04.570 align:middle line:84% auction where there's this common value 00:56:04.570 --> 00:56:06.250 align:middle line:90% that everyone has for winning. 00:56:06.250 --> 00:56:09.260 align:middle line:90% We all submit our bids. 00:56:09.260 --> 00:56:11.540 align:middle line:84% And then I find out that I've won the bidding. 00:56:11.540 --> 00:56:14.040 align:middle line:84% When I find out that I've won the bidding, what I'm learning 00:56:14.040 --> 00:56:17.140 align:middle line:84% is that my geologist was more optimistic than everybody else's 00:56:17.140 --> 00:56:18.290 align:middle line:90% geologists. 00:56:18.290 --> 00:56:21.430 align:middle line:84% And so particularly if there are n other geologists and n is 00:56:21.430 --> 00:56:24.520 align:middle line:84% a large number, I've learned that my guy was out in the tails 00:56:24.520 --> 00:56:28.360 align:middle line:84% in how he read the seismograph, which then tells me 00:56:28.360 --> 00:56:30.400 align:middle line:84% that this is what people call the winner's 00:56:30.400 --> 00:56:33.070 align:middle line:84% curse, that once I've learned that I win the auction, 00:56:33.070 --> 00:56:36.082 align:middle line:84% I now think the good is worth much less than I thought when I 00:56:36.082 --> 00:56:37.540 align:middle line:84% was submitting my bid, because I've 00:56:37.540 --> 00:56:42.370 align:middle line:84% learned that everybody else's estimate was lower than mine. 00:56:42.370 --> 00:56:47.050 align:middle line:84% Now, in a rational model, it's not 00:56:47.050 --> 00:56:51.130 align:middle line:84% like bidders get negative value because of the winner's curse. 00:56:51.130 --> 00:56:52.900 align:middle line:84% In a rational model, what bidders do is 00:56:52.900 --> 00:56:54.442 align:middle line:84% they account for this in the winning. 00:56:54.442 --> 00:56:58.030 align:middle line:84% They're like, OK, I think there's $50 million worth of oil 00:56:58.030 --> 00:56:58.750 align:middle line:90% there. 00:56:58.750 --> 00:57:02.570 align:middle line:84% But what would I think if I learned that everybody else's 00:57:02.570 --> 00:57:05.420 align:middle line:84% geologists thought there was less oil than mine thought 00:57:05.420 --> 00:57:06.060 align:middle line:90% there was? 00:57:06.060 --> 00:57:08.510 align:middle line:84% And so what you bid is you bid based 00:57:08.510 --> 00:57:14.550 align:middle line:84% on what you think the value is conditional on learning 00:57:14.550 --> 00:57:18.430 align:middle line:84% that everybody else's geologist was less optimistic than yours. 00:57:18.430 --> 00:57:21.690 align:middle line:84% So what you bid on is you're not bidding based on your-- 00:57:21.690 --> 00:57:23.770 align:middle line:84% so in a second price sealed bid auction, 00:57:23.770 --> 00:57:26.100 align:middle line:84% I'm not bidding what's my expected 00:57:26.100 --> 00:57:28.710 align:middle line:90% value conditional on my signal. 00:57:28.710 --> 00:57:33.090 align:middle line:84% I'm bidding what's my expected value conditional on my signal 00:57:33.090 --> 00:57:38.040 align:middle line:84% and on sj less than or equal to si for all j. 00:57:38.040 --> 00:57:42.000 align:middle line:84% And actually in terms of sj equal si for some j, 00:57:42.000 --> 00:57:44.320 align:middle line:90% but it's more complicated. 00:57:44.320 --> 00:57:45.900 align:middle line:84% But anyway, what I'm bidding on, I'm 00:57:45.900 --> 00:57:48.120 align:middle line:84% bidding on what do I think it's worth 00:57:48.120 --> 00:57:53.700 align:middle line:84% knowing that everybody else is bidding has a worse signal 00:57:53.700 --> 00:57:54.490 align:middle line:90% than I do. 00:57:54.490 --> 00:57:57.130 align:middle line:84% And actually knowing that it actually matters what I bid. 00:57:57.130 --> 00:57:59.130 align:middle line:84% So there's somebody else who's very close to me. 00:57:59.130 --> 00:58:01.842 align:middle line:90% 00:58:01.842 --> 00:58:03.300 align:middle line:84% So what rational players will do is 00:58:03.300 --> 00:58:07.830 align:middle line:84% they avoid the winner's curse by just down weighting their bids 00:58:07.830 --> 00:58:09.780 align:middle line:84% based on the amount of winner's curse 00:58:09.780 --> 00:58:13.780 align:middle line:84% that they expect to occur once they learn that they won. 00:58:13.780 --> 00:58:19.140 align:middle line:84% So what I want to do is finish today with one empirical paper. 00:58:19.140 --> 00:58:22.300 align:middle line:84% So this is about winner's curses in auction. 00:58:22.300 --> 00:58:24.300 align:middle line:84% So paper, Hendricks and Porter, empirical study 00:58:24.300 --> 00:58:26.760 align:middle line:84% of an auction with asymmetric information. 00:58:26.760 --> 00:58:31.020 align:middle line:84% This is about US auctions of leases 00:58:31.020 --> 00:58:35.465 align:middle line:84% to drill for oil in waters off the US Coast. 00:58:35.465 --> 00:58:38.183 align:middle line:90% 00:58:38.183 --> 00:58:40.350 align:middle line:84% Most of this oil drilling that they're talking about 00:58:40.350 --> 00:58:43.380 align:middle line:84% is if you go to the Gulf Coast of the United States, 00:58:43.380 --> 00:58:46.800 align:middle line:84% off the Coast of Texas, Louisiana, there are many, 00:58:46.800 --> 00:58:52.327 align:middle line:84% many, many offshore oil wells and in relatively shallow water 00:58:52.327 --> 00:58:53.910 align:middle line:84% where the government has auctioned off 00:58:53.910 --> 00:58:56.640 align:middle line:90% the right to drill for oil. 00:58:56.640 --> 00:58:58.800 align:middle line:84% The US government auctions off two different types 00:58:58.800 --> 00:59:00.160 align:middle line:90% of offshore oil leases. 00:59:00.160 --> 00:59:02.800 align:middle line:84% One are what are called wildcat tracts. 00:59:02.800 --> 00:59:09.400 align:middle line:84% Wildcat tracts are roughly 5,000 acre plots that don't abut any 00:59:09.400 --> 00:59:10.730 align:middle line:90% other drilling. 00:59:10.730 --> 00:59:16.930 align:middle line:84% And about 35% of those wildcat tracts that are bought 00:59:16.930 --> 00:59:19.090 align:middle line:90% end up producing any oil. 00:59:19.090 --> 00:59:21.520 align:middle line:84% The others, either the company doesn't drill them 00:59:21.520 --> 00:59:24.820 align:middle line:84% because doing a more detailed geological survey after they've 00:59:24.820 --> 00:59:27.730 align:middle line:84% won the auction, they decide it's not even worth drilling. 00:59:27.730 --> 00:59:29.380 align:middle line:84% Or they drill a hole and they spend 00:59:29.380 --> 00:59:31.450 align:middle line:84% millions of dollars drilling underground 00:59:31.450 --> 00:59:34.660 align:middle line:84% and then they don't find oil when they drill. 00:59:34.660 --> 00:59:38.080 align:middle line:84% The second type of things that are auctioned 00:59:38.080 --> 00:59:41.140 align:middle line:84% is that I'll just go out here in the Gulf of Mexico 00:59:41.140 --> 00:59:43.460 align:middle line:84% and they'll just auction off the right to drill here. 00:59:43.460 --> 00:59:45.543 align:middle line:84% But then sometimes what happens is you auction off 00:59:45.543 --> 00:59:48.520 align:middle line:84% the right to drill on this tract and there is oil there. 00:59:48.520 --> 00:59:51.820 align:middle line:84% And if there is oil there, then immediately people 00:59:51.820 --> 00:59:57.448 align:middle line:84% tend to want to drill here or here or here or here or here. 00:59:57.448 --> 00:59:58.990 align:middle line:84% Because if you know there's oil here, 00:59:58.990 --> 01:00:01.820 align:middle line:84% there's probably oil nearby also. 01:00:01.820 --> 01:00:05.290 align:middle line:84% And so they also auction off what they call drainage tracts. 01:00:05.290 --> 01:00:08.740 align:middle line:84% They're smaller plots that are adjacent to a previously 01:00:08.740 --> 01:00:10.640 align:middle line:90% drilled wildcat tract. 01:00:10.640 --> 01:00:13.603 align:middle line:84% And so when people buy drainage tracts, 01:00:13.603 --> 01:00:15.770 align:middle line:84% it's more likely that there's going to be oil there. 01:00:15.770 --> 01:00:19.360 align:middle line:84% It's much less risky, much higher expected amount of oil, 01:00:19.360 --> 01:00:23.485 align:middle line:84% because you know there's oil right next door. 01:00:23.485 --> 01:00:27.850 align:middle line:90% 01:00:27.850 --> 01:00:31.150 align:middle line:90% Here's just a map showing-- 01:00:31.150 --> 01:00:36.260 align:middle line:84% here's random wildcat tract that someone is planning to drill on. 01:00:36.260 --> 01:00:39.470 align:middle line:84% This would be an area where, say, this tract was drilled. 01:00:39.470 --> 01:00:40.510 align:middle line:90% They had oil. 01:00:40.510 --> 01:00:42.010 align:middle line:84% And then they started auctioning off 01:00:42.010 --> 01:00:44.890 align:middle line:84% all these little drainage tracts around it 01:00:44.890 --> 01:00:46.780 align:middle line:84% where people can think if there's oil here, 01:00:46.780 --> 01:00:51.950 align:middle line:84% there's probably oil here and all these other places nearby. 01:00:51.950 --> 01:00:56.220 align:middle line:84% And asymmetric information that the winner's curse, they note, 01:00:56.220 --> 01:00:59.370 align:middle line:84% is that this auction is very asymmetric 01:00:59.370 --> 01:01:02.340 align:middle line:84% auction in that there's one firm that 01:01:02.340 --> 01:01:08.340 align:middle line:84% has a well in the ground at this location that knows something 01:01:08.340 --> 01:01:10.930 align:middle line:84% about the oil that they're pumping out of it. 01:01:10.930 --> 01:01:13.560 align:middle line:84% And then there are all these people around here 01:01:13.560 --> 01:01:16.140 align:middle line:84% who don't have the same information that this person 01:01:16.140 --> 01:01:18.160 align:middle line:90% with the wildcat tract is here. 01:01:18.160 --> 01:01:22.980 align:middle line:84% And particularly, the way my understanding of oil drilling 01:01:22.980 --> 01:01:27.040 align:middle line:84% is, oil drilling is a fairly sophisticated thing. 01:01:27.040 --> 01:01:29.370 align:middle line:84% So you've got this thing that's underwater. 01:01:29.370 --> 01:01:32.070 align:middle line:84% I've got my well here that I'm drilling down. 01:01:32.070 --> 01:01:33.990 align:middle line:84% I'm going underwater, and then I'm 01:01:33.990 --> 01:01:36.030 align:middle line:84% drilling into the ground on my wildcat. 01:01:36.030 --> 01:01:39.912 align:middle line:90% So I own this wildcat tract. 01:01:39.912 --> 01:01:43.128 align:middle line:84% You can actually send a drill bit diagonally underground. 01:01:43.128 --> 01:01:44.920 align:middle line:84% So you don't have to drill a straight hole. 01:01:44.920 --> 01:01:46.210 align:middle line:90% You can drill like this. 01:01:46.210 --> 01:01:48.480 align:middle line:90% You can drill like this. 01:01:48.480 --> 01:01:52.400 align:middle line:84% And so imagine that this firm is here. 01:01:52.400 --> 01:01:54.150 align:middle line:84% They're producing a ton of oil from a well 01:01:54.150 --> 01:01:56.370 align:middle line:84% that you know on the surface is up there. 01:01:56.370 --> 01:02:00.082 align:middle line:84% And then they propose that there's 01:02:00.082 --> 01:02:02.790 align:middle line:84% an auction going to be conducted not only for this wildcat tract, 01:02:02.790 --> 01:02:03.540 align:middle line:90% but for this. 01:02:03.540 --> 01:02:05.080 align:middle line:90% So this is the wildcat tract. 01:02:05.080 --> 01:02:06.490 align:middle line:90% There's a drainage tract here. 01:02:06.490 --> 01:02:08.020 align:middle line:90% There's a drainage tract here. 01:02:08.020 --> 01:02:10.380 align:middle line:84% And you're going to bid against ExxonMobil, 01:02:10.380 --> 01:02:13.470 align:middle line:84% who's got their pipe in the ground, pumping a ton of oil 01:02:13.470 --> 01:02:14.557 align:middle line:90% out of this wildcat tract. 01:02:14.557 --> 01:02:16.640 align:middle line:84% And let's suppose that you're bidding against them 01:02:16.640 --> 01:02:19.223 align:middle line:84% and you're like, OK, I'm going to bid for this drainage tract. 01:02:19.223 --> 01:02:21.000 align:middle line:84% And what you learn is that they didn't 01:02:21.000 --> 01:02:22.360 align:middle line:90% bid for that drainage tract. 01:02:22.360 --> 01:02:24.120 align:middle line:84% They bid for that drainage tract. 01:02:24.120 --> 01:02:25.680 align:middle line:84% As soon as you learn that ExxonMobil 01:02:25.680 --> 01:02:27.000 align:middle line:84% bid for this drainage tract, you think 01:02:27.000 --> 01:02:29.820 align:middle line:84% it must be that what they did is they drilled a thing down here 01:02:29.820 --> 01:02:31.390 align:middle line:84% and they went diagonally that way. 01:02:31.390 --> 01:02:33.240 align:middle line:84% So they think there's oil over here. 01:02:33.240 --> 01:02:35.560 align:middle line:84% I've just won this drainage tract. 01:02:35.560 --> 01:02:38.730 align:middle line:84% Do I even want to drill it once I've learned that ExxonMobil 01:02:38.730 --> 01:02:42.350 align:middle line:90% didn't want this one? 01:02:42.350 --> 01:02:46.460 align:middle line:84% Anyway, so that creates the potential for a severe winner's 01:02:46.460 --> 01:02:49.250 align:middle line:84% curse and that the person who has the pipe in the ground 01:02:49.250 --> 01:02:51.800 align:middle line:84% knows much more about the oil pressure 01:02:51.800 --> 01:02:55.085 align:middle line:84% and about where the oil is coming from than all the firms 01:02:55.085 --> 01:02:56.960 align:middle line:84% who are just able to observe that they've got 01:02:56.960 --> 01:03:01.760 align:middle line:84% a rig set up here in the middle of the ocean somewhere. 01:03:01.760 --> 01:03:05.030 align:middle line:84% One thing that's interesting about this is so these drainage 01:03:05.030 --> 01:03:08.600 align:middle line:84% tracts, if you look at the fraction that are productive, 01:03:08.600 --> 01:03:11.720 align:middle line:84% and I guess it's even really hard to see this, 01:03:11.720 --> 01:03:14.100 align:middle line:84% so there were 1,000 in this data set. 01:03:14.100 --> 01:03:15.900 align:middle line:90% There were 1,056 wildcat tracks. 01:03:15.900 --> 01:03:17.940 align:middle line:90% Only 385 had oil. 01:03:17.940 --> 01:03:20.120 align:middle line:90% There were 144 drainage tracks. 01:03:20.120 --> 01:03:21.210 align:middle line:90% 86 had oil. 01:03:21.210 --> 01:03:24.050 align:middle line:84% So it's much higher fraction have oil. 01:03:24.050 --> 01:03:27.030 align:middle line:84% The average value of the oil taken out of them, 01:03:27.030 --> 01:03:29.343 align:middle line:84% these tracts have an average of 5.27-- 01:03:29.343 --> 01:03:31.010 align:middle line:84% I guess it must be millions of something 01:03:31.010 --> 01:03:33.210 align:middle line:90% or other dollars in oil. 01:03:33.210 --> 01:03:38.370 align:middle line:84% The drainage tracts have $13.5 million of value on average. 01:03:38.370 --> 01:03:42.500 align:middle line:84% Yet somehow the wildcat tracts attract 3 and 1/2 bidders per 01:03:42.500 --> 01:03:43.140 align:middle line:90% auction. 01:03:43.140 --> 01:03:47.250 align:middle line:84% The drainage tracts attract only 2.7 bidders per auction. 01:03:47.250 --> 01:03:50.210 align:middle line:84% So you have these much more valuable tracts 01:03:50.210 --> 01:03:54.080 align:middle line:84% that are much lower risk and yet attract fewer bidders 01:03:54.080 --> 01:03:55.860 align:middle line:90% than the wildcat tracts. 01:03:55.860 --> 01:03:58.580 align:middle line:84% And as a result, unsurprisingly, the average profits 01:03:58.580 --> 01:04:00.680 align:middle line:84% earned by the winning bidder are much higher 01:04:00.680 --> 01:04:05.010 align:middle line:84% in bidding for drainage tracts than bidding for wildcat tracts. 01:04:05.010 --> 01:04:07.260 align:middle line:84% And Hendricks and Porter started to note, 01:04:07.260 --> 01:04:09.990 align:middle line:84% isn't this initially seem like a puzzle? 01:04:09.990 --> 01:04:12.270 align:middle line:84% Why would the drainage tracts that 01:04:12.270 --> 01:04:15.240 align:middle line:84% are so much more reliable and so much more profitable 01:04:15.240 --> 01:04:18.930 align:middle line:84% have fewer bidders and much higher profits than the wildcat 01:04:18.930 --> 01:04:20.460 align:middle line:90% ones where it's highly risky? 01:04:20.460 --> 01:04:23.203 align:middle line:84% And they suggest that this is a natural consequence 01:04:23.203 --> 01:04:24.120 align:middle line:90% of the winner's curse. 01:04:24.120 --> 01:04:27.540 align:middle line:84% That the because the winner's curse is so severe, 01:04:27.540 --> 01:04:30.930 align:middle line:84% everybody is afraid to bid against the incumbent who's 01:04:30.930 --> 01:04:33.360 align:middle line:84% already extracting the oil from the wildcat tract. 01:04:33.360 --> 01:04:36.360 align:middle line:84% And therefore, the incumbents earn high profits 01:04:36.360 --> 01:04:38.015 align:middle line:84% on these tracts and other people just 01:04:38.015 --> 01:04:39.390 align:middle line:84% tend to stay away because they're 01:04:39.390 --> 01:04:40.598 align:middle line:90% afraid of the winner's curse. 01:04:40.598 --> 01:04:45.130 align:middle line:90% 01:04:45.130 --> 01:04:46.520 align:middle line:90% So it's a nice idea. 01:04:46.520 --> 01:04:48.850 align:middle line:84% But in some ways, I think I wanted 01:04:48.850 --> 01:04:51.430 align:middle line:84% to cover Hendricks and Porter is it's 01:04:51.430 --> 01:04:55.900 align:middle line:84% a really beautiful example of how you can write a reduced form 01:04:55.900 --> 01:05:00.640 align:middle line:84% empirical IO paper in that they start with of simple idea 01:05:00.640 --> 01:05:03.490 align:middle line:84% of people are afraid of the winner's curse, 01:05:03.490 --> 01:05:04.940 align:middle line:90% therefore they bid less. 01:05:04.940 --> 01:05:07.120 align:middle line:84% And what they try to do is build that out as-- 01:05:07.120 --> 01:05:09.580 align:middle line:84% write down a model and then think 01:05:09.580 --> 01:05:13.303 align:middle line:84% of seven different implications of the model that are not 01:05:13.303 --> 01:05:15.970 align:middle line:84% obvious from when you just state the model, and then think about 01:05:15.970 --> 01:05:17.830 align:middle line:90% are those implications all true. 01:05:17.830 --> 01:05:20.650 align:middle line:84% And use that to decide, is the asymmetric information 01:05:20.650 --> 01:05:22.810 align:middle line:84% really the explanation here, or could there 01:05:22.810 --> 01:05:24.440 align:middle line:90% be some different explanation? 01:05:24.440 --> 01:05:26.773 align:middle line:84% They don't work out what the alternate explanations are, 01:05:26.773 --> 01:05:29.422 align:middle line:84% but the thought is if I have my one explanation, 01:05:29.422 --> 01:05:31.630 align:middle line:84% my one explanation makes seven different predictions. 01:05:31.630 --> 01:05:33.770 align:middle line:84% I can then test my seven different predictions, 01:05:33.770 --> 01:05:35.560 align:middle line:84% if they seem to hold, then I think this 01:05:35.560 --> 01:05:37.430 align:middle line:90% is a good explanation for this. 01:05:37.430 --> 01:05:39.680 align:middle line:90% So here's a very simple model. 01:05:39.680 --> 01:05:43.090 align:middle line:84% So they have a wildcat tract that 01:05:43.090 --> 01:05:46.220 align:middle line:84% has one informed person who's drilling on the wildcat tract, 01:05:46.220 --> 01:05:48.325 align:middle line:84% and then there's a single drainage tract nearby. 01:05:48.325 --> 01:05:50.450 align:middle line:84% They're going to assume that the drainage tract has 01:05:50.450 --> 01:05:54.260 align:middle line:84% value v to the person who is already 01:05:54.260 --> 01:05:57.840 align:middle line:84% drilling the wildcat tract and v minus c to the others. 01:05:57.840 --> 01:06:00.050 align:middle line:84% So the option is not only does ExxonMobil have 01:06:00.050 --> 01:06:02.120 align:middle line:90% an informational advantage. 01:06:02.120 --> 01:06:05.630 align:middle line:84% ExxonMobil would get v if they win the drainage tract, 01:06:05.630 --> 01:06:08.450 align:middle line:84% whereas a rival would only get v minus c. 01:06:08.450 --> 01:06:10.010 align:middle line:84% And the thought is that the rivals 01:06:10.010 --> 01:06:13.250 align:middle line:84% are getting less value because when you already have a platform 01:06:13.250 --> 01:06:15.290 align:middle line:84% nearby, there's economies of scale 01:06:15.290 --> 01:06:17.340 align:middle line:84% and building a second platform here. 01:06:17.340 --> 01:06:20.490 align:middle line:84% And so there's a cost advantage as well 01:06:20.490 --> 01:06:25.760 align:middle line:84% that might explain why ExxonMobil will bid more. 01:06:25.760 --> 01:06:28.050 align:middle line:90% We have n uninformed bidders. 01:06:28.050 --> 01:06:30.770 align:middle line:84% The uninformed bidders do get some signal. 01:06:30.770 --> 01:06:33.050 align:middle line:84% They get some signal z, which can 01:06:33.050 --> 01:06:34.650 align:middle line:84% be the signal from their geologists. 01:06:34.650 --> 01:06:37.092 align:middle line:84% It could be the signal from ExxonMobil 01:06:37.092 --> 01:06:39.800 align:middle line:84% does have to report how much oil they're pulling out of that well 01:06:39.800 --> 01:06:41.292 align:middle line:90% because they pay royalties. 01:06:41.292 --> 01:06:43.250 align:middle line:84% And they're going to assume that this satisfies 01:06:43.250 --> 01:06:45.950 align:middle line:84% the expected value is bigger than the government's reserve 01:06:45.950 --> 01:06:47.090 align:middle line:90% price. 01:06:47.090 --> 01:06:50.690 align:middle line:84% The expected value is increasing in the quality of their signal. 01:06:50.690 --> 01:06:52.640 align:middle line:84% But there's always some probability 01:06:52.640 --> 01:06:55.010 align:middle line:84% that the value will be less than the reserve price, 01:06:55.010 --> 01:06:58.630 align:middle line:84% no matter how positive the signal is. 01:06:58.630 --> 01:07:00.910 align:middle line:84% And then you have the one informed firm 01:07:00.910 --> 01:07:05.290 align:middle line:84% that both sees the true value, actually fully knows 01:07:05.290 --> 01:07:07.450 align:middle line:84% how much oil is under the drainage tract, 01:07:07.450 --> 01:07:10.480 align:middle line:84% and sees the signal that the uninformed bidders 01:07:10.480 --> 01:07:11.710 align:middle line:90% are relying on. 01:07:11.710 --> 01:07:14.830 align:middle line:84% And then they think about a first price sealed bid auction 01:07:14.830 --> 01:07:16.395 align:middle line:90% with a reservation price of r. 01:07:16.395 --> 01:07:20.270 align:middle line:90% 01:07:20.270 --> 01:07:22.590 align:middle line:84% Observation like we've done a few times in this class. 01:07:22.590 --> 01:07:26.900 align:middle line:84% This is not a game that can have a pure strategy equilibrium. 01:07:26.900 --> 01:07:30.260 align:middle line:84% Because in a pure strategy equilibrium in some sense, 01:07:30.260 --> 01:07:32.210 align:middle line:84% the firm playing the uninformed guys 01:07:32.210 --> 01:07:34.040 align:middle line:84% are just too vulnerable when they 01:07:34.040 --> 01:07:35.490 align:middle line:90% play pure strategy equilibrium. 01:07:35.490 --> 01:07:38.750 align:middle line:84% So you can't have an equilibrium where the uninformed bidders are 01:07:38.750 --> 01:07:41.570 align:middle line:84% not bidding, because the uninformed guys were not 01:07:41.570 --> 01:07:44.450 align:middle line:84% bidding, the informed guy would just bid r. 01:07:44.450 --> 01:07:47.750 align:middle line:84% And then bidding r plus epsilon would be a profitable deviation 01:07:47.750 --> 01:07:50.180 align:middle line:84% for the uninformed bidders, because on average, the tracts 01:07:50.180 --> 01:07:51.530 align:middle line:90% are worth a lot. 01:07:51.530 --> 01:07:53.930 align:middle line:84% So you can't have the uninformed bidders not bidding, 01:07:53.930 --> 01:07:56.030 align:middle line:84% because then the informed bidder would bid r, 01:07:56.030 --> 01:07:57.863 align:middle line:84% and then the uninformed guys would wish they 01:07:57.863 --> 01:07:59.340 align:middle line:90% were bidding r plus epsilon. 01:07:59.340 --> 01:08:02.480 align:middle line:84% And so that can't be an equilibrium. 01:08:02.480 --> 01:08:04.460 align:middle line:84% You also can't have an equilibrium where 01:08:04.460 --> 01:08:06.230 align:middle line:84% the uninformed guys are following 01:08:06.230 --> 01:08:12.080 align:middle line:84% some pure strategy that's some function b uninformed of z. 01:08:12.080 --> 01:08:15.050 align:middle line:84% Because if they were playing this pure strategy, 01:08:15.050 --> 01:08:16.837 align:middle line:84% then what would the incumbent do? 01:08:16.837 --> 01:08:18.920 align:middle line:84% If the value was bigger than what they're bidding, 01:08:18.920 --> 01:08:20.340 align:middle line:90% the incumbent would take it. 01:08:20.340 --> 01:08:22.100 align:middle line:84% And if the value was less than what they're bidding, 01:08:22.100 --> 01:08:23.750 align:middle line:84% the incumbent will leave it to them. 01:08:23.750 --> 01:08:26.330 align:middle line:84% So basically, if they're playing a pure strategy, 01:08:26.330 --> 01:08:27.560 align:middle line:90% they always lose. 01:08:27.560 --> 01:08:30.020 align:middle line:84% Because either the incumbent, it's a good tract 01:08:30.020 --> 01:08:32.844 align:middle line:84% and the incumbent takes it from them, or it's a bad tract 01:08:32.844 --> 01:08:34.819 align:middle line:84% and the incumbent leaves it with them. 01:08:34.819 --> 01:08:37.100 align:middle line:84% So you can't have any of these equilibria. 01:08:37.100 --> 01:08:40.170 align:middle line:84% What do you get in these models of search? 01:08:40.170 --> 01:08:42.800 align:middle line:84% You get a mixed strategy equilibria. 01:08:42.800 --> 01:08:45.180 align:middle line:84% So the uninformed bidders are going to mix. 01:08:45.180 --> 01:08:47.115 align:middle line:84% Sometimes they're going to bid exactly 0 01:08:47.115 --> 01:08:48.740 align:middle line:84% and sometimes they're going to mix over 01:08:48.740 --> 01:08:50.810 align:middle line:90% the interval from r to z. 01:08:50.810 --> 01:08:54.960 align:middle line:84% And their mixing is going to be such 01:08:54.960 --> 01:08:56.946 align:middle line:84% that it forces the incumbent to play. 01:08:56.946 --> 01:08:59.279 align:middle line:84% It's optimal for the incumbent to play a strategy, which 01:08:59.279 --> 01:09:04.140 align:middle line:84% is if there's no oil bid 0, if v is a little bit bigger 01:09:04.140 --> 01:09:06.660 align:middle line:84% than the reserve price and z is not too big, then just 01:09:06.660 --> 01:09:08.740 align:middle line:90% bid exactly the reserve price. 01:09:08.740 --> 01:09:13.830 align:middle line:84% And then as either the value gets larger 01:09:13.830 --> 01:09:15.840 align:middle line:84% or z gets bigger, start to increase your bid 01:09:15.840 --> 01:09:18.210 align:middle line:90% and bid above the reserve price. 01:09:18.210 --> 01:09:21.359 align:middle line:84% So the incumbent is, if I think about what the incumbent's bid 01:09:21.359 --> 01:09:25.050 align:middle line:84% distribution looks like, sometimes I 01:09:25.050 --> 01:09:27.569 align:middle line:84% see the incumbent bidding exactly 0. 01:09:27.569 --> 01:09:28.840 align:middle line:90% Sorry, bidding exactly 0. 01:09:28.840 --> 01:09:30.279 align:middle line:90% Just not even bidding. 01:09:30.279 --> 01:09:33.210 align:middle line:84% Sometimes I see the incumbent bidding the reserve price. 01:09:33.210 --> 01:09:35.640 align:middle line:84% And then there's going to be some density of bids where 01:09:35.640 --> 01:09:39.060 align:middle line:84% the incumbent bids more if it knows the tract is highly 01:09:39.060 --> 01:09:40.890 align:middle line:90% valuable and looks attractive. 01:09:40.890 --> 01:09:44.760 align:middle line:84% It's going to bid a higher amount. 01:09:44.760 --> 01:09:47.910 align:middle line:84% So this is what the incumbent does. 01:09:47.910 --> 01:09:51.100 align:middle line:90% What do the uninformed guys do? 01:09:51.100 --> 01:09:54.710 align:middle line:84% The uninformed guys are playing a corresponding mixture. 01:09:54.710 --> 01:09:58.330 align:middle line:84% They don't know anything, but sometimes they bid 0 01:09:58.330 --> 01:10:02.910 align:middle line:84% and then they also bid over some distribution of higher values. 01:10:02.910 --> 01:10:06.060 align:middle line:90% 01:10:06.060 --> 01:10:07.330 align:middle line:90% Let me be more realistic. 01:10:07.330 --> 01:10:09.920 align:middle line:84% Maybe they bid 0 a lot because they're scared. 01:10:09.920 --> 01:10:12.980 align:middle line:90% 01:10:12.980 --> 01:10:18.380 align:middle line:84% So anyway, Hendricks and Porter solve for that equilibrium. 01:10:18.380 --> 01:10:21.170 align:middle line:84% And a very nice feature is that they 01:10:21.170 --> 01:10:23.210 align:middle line:84% have many different predictions that they 01:10:23.210 --> 01:10:24.840 align:middle line:90% can derive in this model. 01:10:24.840 --> 01:10:29.660 align:middle line:84% So the first one is that in this equilibrium, 01:10:29.660 --> 01:10:33.110 align:middle line:84% the incumbents bid 0 with a smaller 01:10:33.110 --> 01:10:37.850 align:middle line:84% probability than the probability that the uninformed guys bid 0. 01:10:37.850 --> 01:10:42.080 align:middle line:84% So 0 bids by the incumbent are less common than 0 bids 01:10:42.080 --> 01:10:45.290 align:middle line:90% by the disadvantaged entrants. 01:10:45.290 --> 01:10:48.445 align:middle line:84% The informed bidder wins the auction at least half the time. 01:10:48.445 --> 01:10:51.090 align:middle line:90% 01:10:51.090 --> 01:10:54.030 align:middle line:84% The uninformed bidders are earning 0 profits 01:10:54.030 --> 01:10:56.730 align:middle line:84% because they're mixing and they're mixing with 0 01:10:56.730 --> 01:10:58.000 align:middle line:90% in the equilibrium support. 01:10:58.000 --> 01:11:00.900 align:middle line:90% So sometimes they do bid 0. 01:11:00.900 --> 01:11:05.960 align:middle line:84% And so profits are 0 in expectation. 01:11:05.960 --> 01:11:07.970 align:middle line:84% In the bad news case where they bid 01:11:07.970 --> 01:11:10.410 align:middle line:84% something and the informed bidder bids 0, 01:11:10.410 --> 01:11:12.330 align:middle line:90% then their profits are negative. 01:11:12.330 --> 01:11:14.810 align:middle line:84% And in the good news case, where the informed bidder 01:11:14.810 --> 01:11:17.180 align:middle line:84% bids at least r, then their profits 01:11:17.180 --> 01:11:19.550 align:middle line:84% are positive in expectation, because they 01:11:19.550 --> 01:11:20.800 align:middle line:90% have 0 expected profits. 01:11:20.800 --> 01:11:22.800 align:middle line:84% In the bad news case, they get negative profits. 01:11:22.800 --> 01:11:26.990 align:middle line:84% They must get positive profits in the good news case. 01:11:26.990 --> 01:11:29.380 align:middle line:84% The incumbent earns positive profits. 01:11:29.380 --> 01:11:32.110 align:middle line:90% 01:11:32.110 --> 01:11:36.580 align:middle line:84% A much less obvious statement is that when the cost 01:11:36.580 --> 01:11:40.780 align:middle line:84% c is close to 0, so the two firms don't have big cost 01:11:40.780 --> 01:11:46.090 align:middle line:84% differences, the ex-ante bid distributions of the incumbents 01:11:46.090 --> 01:11:50.530 align:middle line:84% and the entrants and the uninformed bidders 01:11:50.530 --> 01:11:52.490 align:middle line:90% converge to each other. 01:11:52.490 --> 01:11:57.265 align:middle line:84% So as c goes to 0, this is a bid distribution 01:11:57.265 --> 01:11:59.890 align:middle line:84% that comes from bidding based on what you know about the value. 01:11:59.890 --> 01:12:02.270 align:middle line:84% This is one that comes purely from randomization. 01:12:02.270 --> 01:12:04.960 align:middle line:84% But these two distributions approach each other 01:12:04.960 --> 01:12:06.070 align:middle line:90% as c goes to 0. 01:12:06.070 --> 01:12:09.160 align:middle line:84% And the c equals 0 limit, these two distributions 01:12:09.160 --> 01:12:10.166 align:middle line:90% would be identical. 01:12:10.166 --> 01:12:14.800 align:middle line:90% 01:12:14.800 --> 01:12:18.550 align:middle line:84% The incumbent's bid is independent of the number 01:12:18.550 --> 01:12:20.560 align:middle line:90% of rival bids. 01:12:20.560 --> 01:12:22.720 align:middle line:84% That's another property of the mixing. 01:12:22.720 --> 01:12:26.440 align:middle line:84% And the incumbent's bid is an increasing function 01:12:26.440 --> 01:12:30.290 align:middle line:84% of the true value of the tract and of the signal that's 01:12:30.290 --> 01:12:34.880 align:middle line:84% available when people are bidding on the tract. 01:12:34.880 --> 01:12:37.130 align:middle line:84% And it's an increasing function of the true value, 01:12:37.130 --> 01:12:38.840 align:middle line:84% because the more it's worth winning, the more aggressive 01:12:38.840 --> 01:12:39.450 align:middle line:90% you want to be. 01:12:39.450 --> 01:12:40.825 align:middle line:84% It's an increasing function of z, 01:12:40.825 --> 01:12:43.807 align:middle line:84% because if you know the opponents are getting better 01:12:43.807 --> 01:12:45.390 align:middle line:84% signals, they're more likely to enter, 01:12:45.390 --> 01:12:48.890 align:middle line:90% you bid more aggressively. 01:12:48.890 --> 01:12:50.840 align:middle line:84% And then what Hendricks and Porter do 01:12:50.840 --> 01:12:53.700 align:middle line:90% is they get this data set. 01:12:53.700 --> 01:12:55.900 align:middle line:84% It's a somewhat historical paper. 01:12:55.900 --> 01:12:59.810 align:middle line:84% They got information on 114 drainage tracts auctioned 01:12:59.810 --> 01:13:02.810 align:middle line:90% between 1959 and 1969. 01:13:02.810 --> 01:13:05.990 align:middle line:84% All of them are adjacent to a wildcat tract on which they 01:13:05.990 --> 01:13:07.252 align:middle line:90% have production data. 01:13:07.252 --> 01:13:09.710 align:middle line:84% And so one of the nice things about going back historically 01:13:09.710 --> 01:13:12.708 align:middle line:84% is they're doing this far enough after the time 01:13:12.708 --> 01:13:14.750 align:middle line:84% all these auctions occurred that they can observe 01:13:14.750 --> 01:13:17.940 align:middle line:84% all the production that occurred over the lifetime of the wells. 01:13:17.940 --> 01:13:21.170 align:middle line:84% So the wells are being drilled over the next five years 01:13:21.170 --> 01:13:23.450 align:middle line:84% after their auction, and then they're producing oil 01:13:23.450 --> 01:13:25.250 align:middle line:84% after some number of years, but they're 01:13:25.250 --> 01:13:28.010 align:middle line:84% able to run out when all the oil got produced 01:13:28.010 --> 01:13:30.715 align:middle line:84% and how valuable things were ex post. 01:13:30.715 --> 01:13:33.910 align:middle line:90% 01:13:33.910 --> 01:13:42.558 align:middle line:84% Anyway, the data include the bids by all the participants, 01:13:42.558 --> 01:13:44.350 align:middle line:84% the number of neighbors bidding, the number 01:13:44.350 --> 01:13:48.280 align:middle line:84% of non-neighbors bidding, the ex post profitability of the tract, 01:13:48.280 --> 01:13:50.020 align:middle line:84% the gross profits of the adjacent tract, 01:13:50.020 --> 01:13:50.925 align:middle line:90% and things like that. 01:13:50.925 --> 01:13:54.987 align:middle line:90% 01:13:54.987 --> 01:13:56.570 align:middle line:84% One of the interesting design features 01:13:56.570 --> 01:13:59.120 align:middle line:84% the US government chose is imagine sometimes you 01:13:59.120 --> 01:14:03.110 align:middle line:90% may have this situation. 01:14:03.110 --> 01:14:08.405 align:middle line:84% So imagine you have ExxonMobil here and you have BP here. 01:14:08.405 --> 01:14:11.840 align:middle line:90% 01:14:11.840 --> 01:14:14.225 align:middle line:84% And then there's a drainage tract right here. 01:14:14.225 --> 01:14:16.100 align:middle line:84% The one case you would think, OK, then you're 01:14:16.100 --> 01:14:17.517 align:middle line:84% going to get a lot of competition. 01:14:17.517 --> 01:14:19.527 align:middle line:84% If ExxonMobil's got this, BP's got this, 01:14:19.527 --> 01:14:21.110 align:middle line:84% they're both producing oil and there's 01:14:21.110 --> 01:14:23.265 align:middle line:90% this little area in between. 01:14:23.265 --> 01:14:24.890 align:middle line:84% Rules the US government set up for this 01:14:24.890 --> 01:14:26.900 align:middle line:84% is that ExxonMobil and BP in that situation 01:14:26.900 --> 01:14:30.530 align:middle line:84% can form a joint venture and bid together jointly on the tract 01:14:30.530 --> 01:14:32.870 align:middle line:84% rather than competing with each other. 01:14:32.870 --> 01:14:36.210 align:middle line:84% So in most cases, in the data set where this occurs, 01:14:36.210 --> 01:14:38.660 align:middle line:84% lo and behold, the firms do form the joint venture and bid 01:14:38.660 --> 01:14:39.560 align:middle line:90% together. 01:14:39.560 --> 01:14:44.570 align:middle line:84% So mostly they have one incumbent tract. 01:14:44.570 --> 01:14:48.440 align:middle line:84% Anyway, so then testing predictions of the model. 01:14:48.440 --> 01:14:50.060 align:middle line:84% Prediction one that the neighbors 01:14:50.060 --> 01:14:52.460 align:middle line:84% are supposed to bid much higher fraction 01:14:52.460 --> 01:14:54.190 align:middle line:90% time than the non-neighbors. 01:14:54.190 --> 01:14:55.540 align:middle line:90% That's borne out in the data. 01:14:55.540 --> 01:14:58.292 align:middle line:84% The neighbors are bidding 83%, the non-neighbors, 68%. 01:14:58.292 --> 01:15:01.110 align:middle line:90% 01:15:01.110 --> 01:15:04.470 align:middle line:84% The incumbents are supposed to win more than half the time. 01:15:04.470 --> 01:15:06.490 align:middle line:90% They're winning 52% of the time. 01:15:06.490 --> 01:15:09.420 align:middle line:84% I don't know if that's such great confirmation. 01:15:09.420 --> 01:15:11.010 align:middle line:84% The uninformed bidders are supposed 01:15:11.010 --> 01:15:15.240 align:middle line:84% to get negative profits if the incumbent enters, 01:15:15.240 --> 01:15:18.000 align:middle line:90% negative profits otherwise. 01:15:18.000 --> 01:15:20.610 align:middle line:84% That's one of the clearer things in the data 01:15:20.610 --> 01:15:26.250 align:middle line:84% that when auctions where the non neighbors win, 01:15:26.250 --> 01:15:30.330 align:middle line:84% you compare the situations where the incumbent bid 01:15:30.330 --> 01:15:32.080 align:middle line:90% and the incumbent didn't bid. 01:15:32.080 --> 01:15:35.170 align:middle line:84% When the incumbent didn't bid, you get very negative profits. 01:15:35.170 --> 01:15:37.423 align:middle line:84% When the incumbent did bid, you get positive profits. 01:15:37.423 --> 01:15:42.510 align:middle line:90% 01:15:42.510 --> 01:15:45.180 align:middle line:84% The incumbents are earning a lot of money. 01:15:45.180 --> 01:15:49.080 align:middle line:84% That was also very clear in this table. 01:15:49.080 --> 01:15:53.310 align:middle line:84% The incumbent win tracts are very high positive profits, 01:15:53.310 --> 01:15:56.140 align:middle line:84% whereas these are essentially 0 on average. 01:15:56.140 --> 01:16:00.930 align:middle line:90% 01:16:00.930 --> 01:16:05.070 align:middle line:84% The bottom part of the paper is where 01:16:05.070 --> 01:16:09.000 align:middle line:84% this starts to seem less high tech econometrically than you 01:16:09.000 --> 01:16:10.050 align:middle line:90% would expect today. 01:16:10.050 --> 01:16:14.070 align:middle line:84% We're trying to see whether these two distributions are 01:16:14.070 --> 01:16:17.070 align:middle line:84% ex-ante identical rather than doing 01:16:17.070 --> 01:16:20.400 align:middle line:84% some kind of non-parametric estimation of the densities 01:16:20.400 --> 01:16:22.030 align:middle line:90% of those distributions. 01:16:22.030 --> 01:16:24.270 align:middle line:84% They're just running some regressions 01:16:24.270 --> 01:16:31.090 align:middle line:84% and asking whether the epsilons seem to have similar variances 01:16:31.090 --> 01:16:35.380 align:middle line:84% and whether the bids seem to be similarly related to the number 01:16:35.380 --> 01:16:37.750 align:middle line:84% once you control for the acres, the number of neighbors, 01:16:37.750 --> 01:16:40.810 align:middle line:90% the values, things like that. 01:16:40.810 --> 01:16:44.140 align:middle line:84% So I don't really know whether that's really 01:16:44.140 --> 01:16:46.510 align:middle line:90% great verification. 01:16:46.510 --> 01:16:51.160 align:middle line:84% Then my prediction six was that the incumbent's bid 01:16:51.160 --> 01:16:53.870 align:middle line:84% doesn't depend on the number of non-incumbents bidding. 01:16:53.870 --> 01:16:57.080 align:middle line:84% That's also held out in a regression. 01:16:57.080 --> 01:17:00.130 align:middle line:84% And then to check that the incumbent bid goes up 01:17:00.130 --> 01:17:05.770 align:middle line:84% in the v and the z, they show the incumbent bid does increase 01:17:05.770 --> 01:17:08.470 align:middle line:84% in the true value of oil that's eventually taken out 01:17:08.470 --> 01:17:12.820 align:middle line:84% of the tract 20 years later and also in the amount of money 01:17:12.820 --> 01:17:14.590 align:middle line:84% that comes out of the wildcat tract, 01:17:14.590 --> 01:17:17.070 align:middle line:84% which is the observable thing that everyone else can see. 01:17:17.070 --> 01:17:20.550 align:middle line:90% 01:17:20.550 --> 01:17:23.860 align:middle line:84% So is that my last slide or do I have more? 01:17:23.860 --> 01:17:24.830 align:middle line:90% Nope, that's it. 01:17:24.830 --> 01:17:29.410 align:middle line:84% So anyway, I think it's a very, very nice example of how 01:17:29.410 --> 01:17:32.110 align:middle line:84% you think about this idea of writing reduced form IO where 01:17:32.110 --> 01:17:35.200 align:middle line:84% you just, here's my model, here's a bunch of predictions 01:17:35.200 --> 01:17:37.270 align:middle line:84% that are not completely obvious, and then 01:17:37.270 --> 01:17:40.030 align:middle line:84% I'm going to look at as many more nuanced predictions 01:17:40.030 --> 01:17:41.820 align:middle line:84% as I can, find that they're true. 01:17:41.820 --> 01:17:43.570 align:middle line:84% And it seems like a pretty convincing case 01:17:43.570 --> 01:17:46.150 align:middle line:84% that we do badly in these auctions because 01:17:46.150 --> 01:17:47.600 align:middle line:90% of the asymmetric information. 01:17:47.600 --> 01:17:48.370 align:middle line:90% Can I say that-- 01:17:48.370 --> 01:17:50.080 align:middle line:84% and sometimes people have criticized 01:17:50.080 --> 01:17:52.080 align:middle line:84% the US government and saying, well, why on Earth 01:17:52.080 --> 01:17:56.763 align:middle line:84% would you give BP and ExxonMobil the ability to jointly bid here? 01:17:56.763 --> 01:17:58.930 align:middle line:84% One way to think about this is, though, maybe that's 01:17:58.930 --> 01:18:00.230 align:middle line:90% actually not so stupid. 01:18:00.230 --> 01:18:02.470 align:middle line:84% Maybe what we want to do on the wildcat tracts 01:18:02.470 --> 01:18:04.763 align:middle line:84% is in some sense it's fine to have 01:18:04.763 --> 01:18:06.430 align:middle line:84% adverse selection on the wildcat tracts, 01:18:06.430 --> 01:18:09.340 align:middle line:84% give all the money away to the person who has the initial-- 01:18:09.340 --> 01:18:11.247 align:middle line:84% sorry, give all the drainage tract profits 01:18:11.247 --> 01:18:13.330 align:middle line:84% away to the person who drilled the initial wildcat 01:18:13.330 --> 01:18:15.763 align:middle line:84% tracts, because the wildcat tracts, 01:18:15.763 --> 01:18:17.680 align:middle line:84% again, were out here in the middle of nowhere. 01:18:17.680 --> 01:18:19.998 align:middle line:84% There it's a symmetric auction model. 01:18:19.998 --> 01:18:21.790 align:middle line:84% So in some sense, what you're doing is just 01:18:21.790 --> 01:18:24.800 align:middle line:84% increasing the prize you get from the symmetric auction model 01:18:24.800 --> 01:18:27.860 align:middle line:84% to be you get the prize, which is all the oil here, 01:18:27.860 --> 01:18:30.930 align:middle line:84% plus the advantage on the surrounding drainage tracts. 01:18:30.930 --> 01:18:33.860 align:middle line:84% And so in some sense, if we just always give you 01:18:33.860 --> 01:18:35.745 align:middle line:84% this big secondary prize, that just 01:18:35.745 --> 01:18:38.120 align:middle line:84% gets competed away in the bidding for the initial wildcat 01:18:38.120 --> 01:18:38.810 align:middle line:90% tracts. 01:18:38.810 --> 01:18:42.020 align:middle line:84% And we can use the competition for the wildcat tracts 01:18:42.020 --> 01:18:44.605 align:middle line:84% as the sensible way to try to raise revenue, 01:18:44.605 --> 01:18:45.980 align:middle line:84% not worrying so much about trying 01:18:45.980 --> 01:18:49.310 align:middle line:84% to get the hard to get drainage tract revenue from the firms 01:18:49.310 --> 01:18:52.220 align:middle line:84% and just bundle it in with the initial wildcat revenue 01:18:52.220 --> 01:18:55.390 align:middle line:84% and then let them bid symmetrically in that case. 01:18:55.390 --> 01:19:08.000 align:middle line:90%