WEBVTT 00:00:00.000 --> 00:00:02.465 align:middle line:90% [SQUEAKING] 00:00:02.465 --> 00:00:04.437 align:middle line:90% [RUSTLING] 00:00:04.437 --> 00:00:11.840 align:middle line:90% [CLICKING] 00:00:11.840 --> 00:00:14.510 align:middle line:84% ROBERT TOWNSEND: OK, so let's look 00:00:14.510 --> 00:00:16.590 align:middle line:90% at where we are in the class. 00:00:16.590 --> 00:00:19.960 align:middle line:90% So this is the class calendar. 00:00:19.960 --> 00:00:23.500 align:middle line:84% So you can see today is virtually kind of the midpoint 00:00:23.500 --> 00:00:25.610 align:middle line:90% of the semester. 00:00:25.610 --> 00:00:27.880 align:middle line:84% Now, the other thing is the reading list. 00:00:27.880 --> 00:00:31.990 align:middle line:84% So today, again, contract theory and mechanism design. 00:00:31.990 --> 00:00:33.880 align:middle line:84% There's only one starred reading. 00:00:33.880 --> 00:00:36.280 align:middle line:84% It's "Rentals with Unobserved Outputs," 00:00:36.280 --> 00:00:38.410 align:middle line:90% this chapter 5 of Medville. 00:00:38.410 --> 00:00:42.820 align:middle line:84% There is a non-starred reading, and I have material 00:00:42.820 --> 00:00:45.460 align:middle line:90% on that in the lecture today. 00:00:45.460 --> 00:00:50.285 align:middle line:84% It's this distributed ledger MIT book, this chapter. 00:00:50.285 --> 00:00:51.910 align:middle line:84% Although I've learned a little bit more 00:00:51.910 --> 00:00:54.730 align:middle line:84% since I wrote the book, which was published yesterday, 00:00:54.730 --> 00:00:58.750 align:middle line:84% and I'll share with you a little bit of that in the lecture. 00:00:58.750 --> 00:01:00.550 align:middle line:90% Anyway, this is all optional. 00:01:00.550 --> 00:01:02.410 align:middle line:84% I'm not quite sure how many of you 00:01:02.410 --> 00:01:04.819 align:middle line:84% have been following Bitcoin and so on. 00:01:04.819 --> 00:01:08.350 align:middle line:84% But as I keep saying, every time an economic topic 00:01:08.350 --> 00:01:10.600 align:middle line:84% comes up that relates to Bitcoin, 00:01:10.600 --> 00:01:13.000 align:middle line:84% as it did with the ledgers last time, 00:01:13.000 --> 00:01:14.990 align:middle line:84% then I weave that into the lecture. 00:01:14.990 --> 00:01:16.940 align:middle line:84% So this is going to be about today. 00:01:16.940 --> 00:01:20.680 align:middle line:84% The second half of the lecture is about smart contracts. 00:01:20.680 --> 00:01:25.200 align:middle line:84% And then for the study guide today, I 00:01:25.200 --> 00:01:29.700 align:middle line:84% can call on a few of you or get volunteers. 00:01:29.700 --> 00:01:33.900 align:middle line:84% Can someone define for me the concept of a household balance 00:01:33.900 --> 00:01:36.900 align:middle line:84% sheet, and also, the income statement? 00:01:36.900 --> 00:01:40.200 align:middle line:84% Just say a few words about what's 00:01:40.200 --> 00:01:44.590 align:middle line:90% on those financial statements. 00:01:44.590 --> 00:01:46.465 align:middle line:84% Armando, do you want to take a crack at that? 00:01:46.465 --> 00:01:50.598 align:middle line:90% 00:01:50.598 --> 00:01:51.640 align:middle line:90% AUDIENCE: Uh, yeah, sure. 00:01:51.640 --> 00:01:57.440 align:middle line:84% So the balance sheet is where you keep track of everything 00:01:57.440 --> 00:01:57.940 align:middle line:90% that-- 00:01:57.940 --> 00:02:01.470 align:middle line:90% 00:02:01.470 --> 00:02:03.990 align:middle line:84% so I'm actually not sure which is which, 00:02:03.990 --> 00:02:06.450 align:middle line:84% but I know one of them involves that you 00:02:06.450 --> 00:02:09.600 align:middle line:84% keep track of your assets and your liabilities. 00:02:09.600 --> 00:02:11.370 align:middle line:84% I believe, yeah, that's the balance sheet. 00:02:11.370 --> 00:02:12.000 align:middle line:90% ROBERT TOWNSEND: Yes. 00:02:12.000 --> 00:02:13.440 align:middle line:84% AUDIENCE: The statement of income 00:02:13.440 --> 00:02:18.330 align:middle line:84% is like all the money in and as well as all the money that 00:02:18.330 --> 00:02:20.750 align:middle line:90% goes out, expenditures. 00:02:20.750 --> 00:02:22.000 align:middle line:90% ROBERT TOWNSEND: That's right. 00:02:22.000 --> 00:02:23.170 align:middle line:90% Good. 00:02:23.170 --> 00:02:24.060 align:middle line:90% OK. 00:02:24.060 --> 00:02:29.080 align:middle line:84% Yeah, the balance sheet has assets on one side, liabilities 00:02:29.080 --> 00:02:29.840 align:middle line:90% on the other. 00:02:29.840 --> 00:02:32.080 align:middle line:90% They don't necessarily balance. 00:02:32.080 --> 00:02:34.510 align:middle line:84% Hopefully, the assets are greater than the liabilities, 00:02:34.510 --> 00:02:36.650 align:middle line:90% and the difference is equity. 00:02:36.650 --> 00:02:38.440 align:middle line:84% So the liability side of the balance sheet 00:02:38.440 --> 00:02:40.390 align:middle line:84% also has an equity component, which 00:02:40.390 --> 00:02:46.180 align:middle line:84% is how much wealth you own that you do not owe to other people 00:02:46.180 --> 00:02:47.230 align:middle line:90% through debt. 00:02:47.230 --> 00:02:51.100 align:middle line:84% The income statement, you stated it properly, yes. 00:02:51.100 --> 00:02:53.710 align:middle line:90% You have revenues and expenses. 00:02:53.710 --> 00:02:55.390 align:middle line:84% Now if you take the difference, you'll 00:02:55.390 --> 00:02:58.840 align:middle line:84% have profits or net income, and then 00:02:58.840 --> 00:03:01.270 align:middle line:84% a couple of other lines on that income statement 00:03:01.270 --> 00:03:06.220 align:middle line:84% were how you dispose of your net income 00:03:06.220 --> 00:03:11.170 align:middle line:84% in terms of either consuming it or saving it. 00:03:11.170 --> 00:03:14.190 align:middle line:84% But your answer was great, thank you. 00:03:14.190 --> 00:03:17.730 align:middle line:84% Then we talked about, in class, life cycle planning. 00:03:17.730 --> 00:03:20.550 align:middle line:84% Can someone tell me what it is exactly? 00:03:20.550 --> 00:03:23.153 align:middle line:84% What we mean by life cycle planning? 00:03:23.153 --> 00:03:24.570 align:middle line:84% AUDIENCE: Can I take a shot at it? 00:03:24.570 --> 00:03:26.040 align:middle line:90% ROBERT TOWNSEND: Yeah, sure. 00:03:26.040 --> 00:03:28.680 align:middle line:84% AUDIENCE: So it's planning what you're actually, 00:03:28.680 --> 00:03:32.350 align:middle line:84% like what choices you're going to make over your entire life. 00:03:32.350 --> 00:03:36.930 align:middle line:84% So you're sort of planning ahead for how much you're 00:03:36.930 --> 00:03:40.530 align:middle line:84% going to spend, like based on your information about what you 00:03:40.530 --> 00:03:43.770 align:middle line:84% expect your income is going to be and stuff like that. 00:03:43.770 --> 00:03:45.270 align:middle line:84% ROBERT TOWNSEND: Yeah, that's good. 00:03:45.270 --> 00:03:45.770 align:middle line:90% Yeah. 00:03:45.770 --> 00:03:48.900 align:middle line:84% It's like and now to, when you die 00:03:48.900 --> 00:03:53.620 align:middle line:84% or when you bequest to your kids or something. 00:03:53.620 --> 00:03:58.390 align:middle line:84% And typically, it's year by year. 00:03:58.390 --> 00:03:59.500 align:middle line:90% And it's kind of-- 00:03:59.500 --> 00:04:01.940 align:middle line:84% I guess I would say the point, I didn't ask this, 00:04:01.940 --> 00:04:05.170 align:middle line:84% but the point of life cycle planning 00:04:05.170 --> 00:04:08.200 align:middle line:84% is to manage your assets in such a way 00:04:08.200 --> 00:04:12.010 align:middle line:84% that your consumption would be as smooth as possible 00:04:12.010 --> 00:04:15.860 align:middle line:90% over the years of your life. 00:04:15.860 --> 00:04:18.640 align:middle line:84% And sometimes you can't achieve that exactly. 00:04:18.640 --> 00:04:21.370 align:middle line:84% The other thing that people associate with a life cycle 00:04:21.370 --> 00:04:25.320 align:middle line:84% planning is an outcome of that process, 00:04:25.320 --> 00:04:29.160 align:middle line:84% namely you have a peak where you're accumulating assets 00:04:29.160 --> 00:04:35.700 align:middle line:84% early on as a young saver with consumption less than income, 00:04:35.700 --> 00:04:40.920 align:middle line:84% and then you start spending down those assets when your income 00:04:40.920 --> 00:04:44.220 align:middle line:84% sources diminish, especially if you retire. 00:04:44.220 --> 00:04:47.490 align:middle line:90% 00:04:47.490 --> 00:04:48.030 align:middle line:90% OK. 00:04:48.030 --> 00:04:50.880 align:middle line:84% And then we applied it to Thailand. 00:04:50.880 --> 00:04:55.590 align:middle line:84% I'm not sure exactly what to ask about. 00:04:55.590 --> 00:04:58.380 align:middle line:84% Well, maybe if one of you could tell me 00:04:58.380 --> 00:05:03.270 align:middle line:84% a special feature of the economic life of Thai villagers 00:05:03.270 --> 00:05:07.140 align:middle line:84% that somehow we incorporated into the life cycle planner 00:05:07.140 --> 00:05:09.330 align:middle line:84% that you would not typically see in the US. 00:05:09.330 --> 00:05:13.040 align:middle line:90% 00:05:13.040 --> 00:05:16.520 align:middle line:90% AUDIENCE: The gift giving? 00:05:16.520 --> 00:05:17.840 align:middle line:90% ROBERT TOWNSEND: Say it again. 00:05:17.840 --> 00:05:20.465 align:middle line:84% AUDIENCE: The gift giving with or without the income. 00:05:20.465 --> 00:05:21.590 align:middle line:90% ROBERT TOWNSEND: Excellent. 00:05:21.590 --> 00:05:24.420 align:middle line:90% That's what I was looking for. 00:05:24.420 --> 00:05:24.920 align:middle line:90% Yeah. 00:05:24.920 --> 00:05:28.010 align:middle line:84% So it looks like an individual operating in isolation, 00:05:28.010 --> 00:05:31.820 align:middle line:84% or at least in most borrowing or lending and acquiring 00:05:31.820 --> 00:05:33.860 align:middle line:84% financial assets, but in Thai villages, 00:05:33.860 --> 00:05:36.500 align:middle line:84% those households interact with one another 00:05:36.500 --> 00:05:38.190 align:middle line:90% by giving gifts and so on. 00:05:38.190 --> 00:05:40.850 align:middle line:84% So the way it was in the equation 00:05:40.850 --> 00:05:44.300 align:middle line:84% was that it smoothed out the downfalls in income 00:05:44.300 --> 00:05:45.980 align:middle line:84% because the gifts would be coming in, 00:05:45.980 --> 00:05:49.890 align:middle line:84% and likewise smoothed over the peaks 00:05:49.890 --> 00:05:53.250 align:middle line:84% because you give those peaks away in terms 00:05:53.250 --> 00:05:56.105 align:middle line:90% of gifts to other people. 00:05:56.105 --> 00:05:56.605 align:middle line:90% OK. 00:05:56.605 --> 00:06:01.880 align:middle line:90% 00:06:01.880 --> 00:06:06.105 align:middle line:84% Can someone tell me what is the concept of a distributed 00:06:06.105 --> 00:06:06.605 align:middle line:90% ledger? 00:06:06.605 --> 00:06:09.680 align:middle line:90% 00:06:09.680 --> 00:06:12.890 align:middle line:84% AUDIENCE: Is it basically just like a publicly recorded, 00:06:12.890 --> 00:06:16.460 align:middle line:84% like where you can have financial transactions be 00:06:16.460 --> 00:06:20.520 align:middle line:84% recorded and available to other people to see? 00:06:20.520 --> 00:06:22.070 align:middle line:90% ROBERT TOWNSEND: Yeah. 00:06:22.070 --> 00:06:26.090 align:middle line:84% So it's a ledger as in an accounting ledger. 00:06:26.090 --> 00:06:29.420 align:middle line:84% It includes a list of transactions. 00:06:29.420 --> 00:06:34.150 align:middle line:84% But in addition to that applying to a given individual, 00:06:34.150 --> 00:06:39.460 align:middle line:84% it's consolidated so that it includes the transactions 00:06:39.460 --> 00:06:43.570 align:middle line:84% in and out as if it were on a common ledger, a ledger that 00:06:43.570 --> 00:06:46.030 align:middle line:84% would apply to all the households 00:06:46.030 --> 00:06:48.640 align:middle line:90% that are participating. 00:06:48.640 --> 00:06:51.790 align:middle line:84% The twist in that is the word distributed. 00:06:51.790 --> 00:06:53.980 align:middle line:84% So although it's common, it's not 00:06:53.980 --> 00:06:57.160 align:middle line:84% supposed to be held by one central party. 00:06:57.160 --> 00:07:00.400 align:middle line:84% Everyone's supposed to have an identical copy of that ledger. 00:07:00.400 --> 00:07:03.490 align:middle line:90% 00:07:03.490 --> 00:07:05.470 align:middle line:84% And in class I complained a little bit 00:07:05.470 --> 00:07:10.600 align:middle line:84% about when we tried to create one for the Thai data. 00:07:10.600 --> 00:07:12.070 align:middle line:90% It didn't quite work. 00:07:12.070 --> 00:07:13.315 align:middle line:90% Does someone remember why? 00:07:13.315 --> 00:07:22.280 align:middle line:90% 00:07:22.280 --> 00:07:25.370 align:middle line:84% Dixon, you want to take a stab at it? 00:07:25.370 --> 00:07:29.660 align:middle line:90% 00:07:29.660 --> 00:07:32.967 align:middle line:84% AUDIENCE: I'm actually not really sure why it didn't work. 00:07:32.967 --> 00:07:33.800 align:middle line:90% ROBERT TOWNSEND: OK. 00:07:33.800 --> 00:07:35.210 align:middle line:90% That's fine. 00:07:35.210 --> 00:07:35.990 align:middle line:90% Anyone else? 00:07:35.990 --> 00:07:40.720 align:middle line:90% 00:07:40.720 --> 00:07:42.730 align:middle line:84% Well, to be fair it was only on one slide 00:07:42.730 --> 00:07:44.450 align:middle line:90% and there was a lot of material. 00:07:44.450 --> 00:07:45.580 align:middle line:90% So let me highlight. 00:07:45.580 --> 00:07:48.350 align:middle line:90% 00:07:48.350 --> 00:07:50.840 align:middle line:84% We didn't have the distributed ledger running 00:07:50.840 --> 00:07:52.350 align:middle line:90% when I collected the data. 00:07:52.350 --> 00:07:55.820 align:middle line:84% Instead, we took the answers the households gave us 00:07:55.820 --> 00:08:00.200 align:middle line:84% to the questionnaires and created financial accounts out 00:08:00.200 --> 00:08:02.200 align:middle line:90% of the answers-- 00:08:02.200 --> 00:08:05.330 align:middle line:84% income statement, balance sheet, and statement of cash flow. 00:08:05.330 --> 00:08:08.830 align:middle line:84% So we had the financial accounts for all the households, 00:08:08.830 --> 00:08:11.590 align:middle line:84% but we didn't try to reconcile them to see if they were 00:08:11.590 --> 00:08:14.650 align:middle line:90% consistent with one another. 00:08:14.650 --> 00:08:18.960 align:middle line:84% So in fact, when they buy something for cash, 00:08:18.960 --> 00:08:22.980 align:middle line:84% they tell us who it was, potentially in the village. 00:08:22.980 --> 00:08:27.370 align:middle line:84% I buy something from J, J should show up 00:08:27.370 --> 00:08:32.860 align:middle line:84% with the same transection where J is selling and getting 00:08:32.860 --> 00:08:35.870 align:middle line:90% cash in return. 00:08:35.870 --> 00:08:37.715 align:middle line:84% So it's one common transection, it 00:08:37.715 --> 00:08:39.340 align:middle line:84% should show up on a distributed ledger. 00:08:39.340 --> 00:08:46.610 align:middle line:84% But because the data didn't try to reconcile all the entries 00:08:46.610 --> 00:08:51.490 align:middle line:84% as they were reported, it was not unusual for one household 00:08:51.490 --> 00:08:53.980 align:middle line:84% to report a transaction with another household 00:08:53.980 --> 00:08:58.890 align:middle line:84% that the other household did not in turn report back. 00:08:58.890 --> 00:09:03.270 align:middle line:84% The point being that distributed ledgers are an excellent way 00:09:03.270 --> 00:09:08.530 align:middle line:84% of reconciling transactions live in real time 00:09:08.530 --> 00:09:11.070 align:middle line:84% so that they become more accurate. 00:09:11.070 --> 00:09:14.380 align:middle line:90% 00:09:14.380 --> 00:09:15.580 align:middle line:90% OK. 00:09:15.580 --> 00:09:19.660 align:middle line:84% And then we went to Thailand and talked about currency, 00:09:19.660 --> 00:09:22.680 align:middle line:90% and there was this-- 00:09:22.680 --> 00:09:27.090 align:middle line:84% the whole lecture was about solving planning problems. 00:09:27.090 --> 00:09:29.100 align:middle line:84% Can someone tell me in words a bit 00:09:29.100 --> 00:09:34.330 align:middle line:84% about this Miller-Orr model of cash management? 00:09:34.330 --> 00:09:36.540 align:middle line:84% AUDIENCE: So in the Miller-Orr model, 00:09:36.540 --> 00:09:40.320 align:middle line:84% the net expenditures are the sum of smaller recurrent 00:09:40.320 --> 00:09:43.920 align:middle line:84% expenditures and infrequent larger ones that 00:09:43.920 --> 00:09:46.800 align:middle line:90% have a lower probability. 00:09:46.800 --> 00:09:50.820 align:middle line:84% And so the goal of the household would be to minimize the cost. 00:09:50.820 --> 00:09:54.632 align:middle line:84% And I remember there was a Bellman equation for that. 00:09:54.632 --> 00:09:55.840 align:middle line:90% ROBERT TOWNSEND: That's good. 00:09:55.840 --> 00:10:00.310 align:middle line:84% You remember the two components of the cost? 00:10:00.310 --> 00:10:05.050 align:middle line:84% AUDIENCE: There was the flow opportunity cost and also 00:10:05.050 --> 00:10:06.463 align:middle line:90% adjustment cost. 00:10:06.463 --> 00:10:07.630 align:middle line:90% ROBERT TOWNSEND: Yeah, yeah. 00:10:07.630 --> 00:10:12.430 align:middle line:84% So the flow opportunity cost is the foregone interest 00:10:12.430 --> 00:10:13.317 align:middle line:90% from holding cash. 00:10:13.317 --> 00:10:15.650 align:middle line:84% If you have currency in the house, it's not in the bank, 00:10:15.650 --> 00:10:18.160 align:middle line:90% it's not earning interest. 00:10:18.160 --> 00:10:20.380 align:middle line:84% So that's kind of the flow of opportunity cost. 00:10:20.380 --> 00:10:23.160 align:middle line:84% And then every time you go to a bank, 00:10:23.160 --> 00:10:26.280 align:middle line:84% either deposit or withdraw the currency, 00:10:26.280 --> 00:10:28.965 align:middle line:84% there is a real transaction cost. 00:10:28.965 --> 00:10:31.790 align:middle line:90% 00:10:31.790 --> 00:10:32.290 align:middle line:90% OK. 00:10:32.290 --> 00:10:41.860 align:middle line:90% 00:10:41.860 --> 00:10:46.110 align:middle line:84% So finally, we get to Kenya and M-Pesa. 00:10:46.110 --> 00:10:51.200 align:middle line:90% Can someone describe for me-- 00:10:51.200 --> 00:10:53.345 align:middle line:90% let's see, who's online here-- 00:10:53.345 --> 00:10:56.840 align:middle line:90% 00:10:56.840 --> 00:11:01.410 align:middle line:84% what exactly is M-Pesa and how it works? 00:11:01.410 --> 00:11:02.630 align:middle line:90% I'll take a volunteer. 00:11:02.630 --> 00:11:07.620 align:middle line:90% 00:11:07.620 --> 00:11:12.780 align:middle line:84% AUDIENCE: I think it's a mobile phone-based money transfer 00:11:12.780 --> 00:11:13.470 align:middle line:90% service. 00:11:13.470 --> 00:11:15.690 align:middle line:84% And you like, pay a small fee and then 00:11:15.690 --> 00:11:20.350 align:middle line:84% you can transfer money to someone else. 00:11:20.350 --> 00:11:24.820 align:middle line:84% It requires trust in the service, I guess. 00:11:24.820 --> 00:11:27.640 align:middle line:84% ROBERT TOWNSEND: What are they actually transferring around 00:11:27.640 --> 00:11:28.720 align:middle line:90% electronically? 00:11:28.720 --> 00:11:31.612 align:middle line:90% 00:11:31.612 --> 00:11:43.130 align:middle line:84% AUDIENCE: Uh, is it not just like, I guess like e-money? 00:11:43.130 --> 00:11:44.380 align:middle line:90% ROBERT TOWNSEND: It's e-money. 00:11:44.380 --> 00:11:45.500 align:middle line:90% It's actually-- 00:11:45.500 --> 00:11:47.938 align:middle line:84% AUDIENCE: It's a telephone, isn't it? 00:11:47.938 --> 00:11:49.480 align:middle line:84% ROBERT TOWNSEND: It's a cell account. 00:11:49.480 --> 00:11:50.440 align:middle line:90% Yes. 00:11:50.440 --> 00:11:51.010 align:middle line:90% That's right. 00:11:51.010 --> 00:11:53.050 align:middle line:90% It's actually credits. 00:11:53.050 --> 00:11:57.760 align:middle line:84% Like you buy credits for phone usage in advance 00:11:57.760 --> 00:12:00.640 align:middle line:90% from Safaricom. 00:12:00.640 --> 00:12:03.813 align:middle line:84% So it's just like you would pay a bill at the end of the month, 00:12:03.813 --> 00:12:05.230 align:middle line:84% they're kind of like paying a bill 00:12:05.230 --> 00:12:06.480 align:middle line:90% at the beginning of the month. 00:12:06.480 --> 00:12:08.770 align:middle line:84% They're buying cell phone credits, 00:12:08.770 --> 00:12:12.010 align:middle line:84% but they don't intend to use it on their cell phone. 00:12:12.010 --> 00:12:14.530 align:middle line:90% Not necessarily. 00:12:14.530 --> 00:12:18.690 align:middle line:84% Instead, they transfer it around, buy things. 00:12:18.690 --> 00:12:22.320 align:middle line:84% And people cash out, they reverse the transaction. 00:12:22.320 --> 00:12:23.445 align:middle line:90% So it's like you can-- 00:12:23.445 --> 00:12:28.770 align:middle line:90% 00:12:28.770 --> 00:12:33.930 align:middle line:84% it's like mileage that you get on an airplane, 00:12:33.930 --> 00:12:36.900 align:middle line:84% but then you can sell your miles. 00:12:36.900 --> 00:12:39.680 align:middle line:84% So they can cash out by selling their e-credit back 00:12:39.680 --> 00:12:40.305 align:middle line:90% to the company. 00:12:40.305 --> 00:12:44.490 align:middle line:90% 00:12:44.490 --> 00:12:47.910 align:middle line:84% So in some respects, it's not so novel. 00:12:47.910 --> 00:12:51.110 align:middle line:84% It's just an electronic account, in this case, 00:12:51.110 --> 00:12:54.800 align:middle line:84% denominated in terms of credits on your cell phone. 00:12:54.800 --> 00:12:57.920 align:middle line:84% But what is novel about it is that it 00:12:57.920 --> 00:13:00.860 align:middle line:84% can be transferred around at very low cost 00:13:00.860 --> 00:13:03.300 align:middle line:84% and you can cash in and cash out. 00:13:03.300 --> 00:13:05.930 align:middle line:84% So it kind of looks like money because you can use it 00:13:05.930 --> 00:13:08.460 align:middle line:90% on your phone like money. 00:13:08.460 --> 00:13:12.680 align:middle line:84% Which then you start to think about it, what is money really? 00:13:12.680 --> 00:13:17.220 align:middle line:84% It doesn't have to be fiat money, the paper stuff. 00:13:17.220 --> 00:13:20.640 align:middle line:84% Like you can have a checking account 00:13:20.640 --> 00:13:24.530 align:middle line:84% in a commercial bank in the US and pay bills 00:13:24.530 --> 00:13:28.100 align:middle line:90% online out of that account. 00:13:28.100 --> 00:13:30.500 align:middle line:84% It's not central bank reserves or fiat money, 00:13:30.500 --> 00:13:33.860 align:middle line:84% but it is money in the sense that it's 00:13:33.860 --> 00:13:36.890 align:middle line:84% used widely in exchange and has a high velocity. 00:13:36.890 --> 00:13:39.620 align:middle line:90% 00:13:39.620 --> 00:13:41.610 align:middle line:84% OK, the trust thing was a good comment 00:13:41.610 --> 00:13:44.100 align:middle line:84% because we're going to come to that today 00:13:44.100 --> 00:13:50.110 align:middle line:84% in the lecture in terms of, in this case, people 00:13:50.110 --> 00:13:53.620 align:middle line:84% trust Safaricom to enter the transactions properly 00:13:53.620 --> 00:13:57.730 align:middle line:84% and to not cheat after the fact, not to steal the money, 00:13:57.730 --> 00:14:01.190 align:middle line:84% and to allow them to cash it out. 00:14:01.190 --> 00:14:02.990 align:middle line:84% But a lot of people are more paranoid 00:14:02.990 --> 00:14:06.900 align:middle line:84% about third party providers, depending on the context. 00:14:06.900 --> 00:14:13.490 align:middle line:84% So we'll get to how to solve that problem today. 00:14:13.490 --> 00:14:16.580 align:middle line:84% So this lecture comes in two halves. 00:14:16.580 --> 00:14:19.610 align:middle line:84% Contract theory and mechanism design is all of it. 00:14:19.610 --> 00:14:21.410 align:middle line:84% The first half is going to feature 00:14:21.410 --> 00:14:25.130 align:middle line:84% an application in-- back to our favorite stomping ground-- 00:14:25.130 --> 00:14:26.780 align:middle line:90% the medieval village economy. 00:14:26.780 --> 00:14:28.790 align:middle line:84% And then as I've already anticipated, 00:14:28.790 --> 00:14:30.350 align:middle line:84% the second half is going to focus 00:14:30.350 --> 00:14:34.520 align:middle line:84% on generalizing the concepts and talking about smart contracts 00:14:34.520 --> 00:14:37.510 align:middle line:90% and validation and trust. 00:14:37.510 --> 00:14:43.380 align:middle line:84% So if you looked at this map, in this case, it's not England, 00:14:43.380 --> 00:14:47.790 align:middle line:84% it's France, you would see these solid filled in circles, 00:14:47.790 --> 00:14:51.900 align:middle line:84% the little Cheerios, and the empty circles, 00:14:51.900 --> 00:14:53.820 align:middle line:90% and small dependent settlements. 00:14:53.820 --> 00:14:59.010 align:middle line:84% So these stand for villas with only demesne, so to speak, 00:14:59.010 --> 00:15:01.170 align:middle line:84% which means everyone worked for the lord 00:15:01.170 --> 00:15:02.760 align:middle line:90% and didn't own their own land. 00:15:02.760 --> 00:15:05.820 align:middle line:84% There are mixed villages that have demesne, 00:15:05.820 --> 00:15:08.890 align:middle line:84% but the households own some of their own land as well. 00:15:08.890 --> 00:15:11.040 align:middle line:84% And then villages where the lord-- 00:15:11.040 --> 00:15:12.810 align:middle line:84% like the Bishop of Winchester in England 00:15:12.810 --> 00:15:15.310 align:middle line:84% doesn't own any of the land at all. 00:15:15.310 --> 00:15:17.400 align:middle line:84% And these are just scattered little hamlets. 00:15:17.400 --> 00:15:22.290 align:middle line:84% So you can start to spot some patterns here. 00:15:22.290 --> 00:15:24.360 align:middle line:84% This is kind of the chief of state 00:15:24.360 --> 00:15:27.240 align:middle line:84% of the lord, the lord of this area; 00:15:27.240 --> 00:15:29.730 align:middle line:84% these little Cheerios surrounding it or halfway 00:15:29.730 --> 00:15:33.900 align:middle line:84% filled in with some land directly farmed for the lord; 00:15:33.900 --> 00:15:35.610 align:middle line:84% and then a little further out you 00:15:35.610 --> 00:15:39.720 align:middle line:84% get these open circles where the lord does not directly 00:15:39.720 --> 00:15:43.290 align:middle line:84% have a claim on the land, although there may be taxes 00:15:43.290 --> 00:15:43.980 align:middle line:90% due. 00:15:43.980 --> 00:15:47.520 align:middle line:84% So that's summarized in this first slide 00:15:47.520 --> 00:15:50.400 align:middle line:84% under alternative forms of organization. 00:15:50.400 --> 00:15:53.970 align:middle line:84% When it's held in demesne only, then essentially the peasant 00:15:53.970 --> 00:15:57.000 align:middle line:90% population are entirely slaves. 00:15:57.000 --> 00:15:59.340 align:middle line:84% And others there was no land like that. 00:15:59.340 --> 00:16:02.190 align:middle line:84% Instead, there were not labor obligations, 00:16:02.190 --> 00:16:06.150 align:middle line:84% but households were obliged to pay rent to the lord 00:16:06.150 --> 00:16:08.230 align:middle line:84% a certain amount of grain that was due. 00:16:08.230 --> 00:16:10.980 align:middle line:84% And we'll come back to what that contract might 00:16:10.980 --> 00:16:11.950 align:middle line:90% have looked like. 00:16:11.950 --> 00:16:15.090 align:middle line:84% And those empty, open circles were really far away 00:16:15.090 --> 00:16:17.340 align:middle line:90% from the central monastery. 00:16:17.340 --> 00:16:20.130 align:middle line:84% So we got three different kinds of organization here. 00:16:20.130 --> 00:16:22.990 align:middle line:84% And theory that we're about to write down is going to say, 00:16:22.990 --> 00:16:25.590 align:middle line:84% well, maybe these forms of organization 00:16:25.590 --> 00:16:27.540 align:middle line:84% varied from one village to the next, 00:16:27.540 --> 00:16:30.390 align:middle line:84% depending on how close they were to the manor, 00:16:30.390 --> 00:16:33.220 align:middle line:84% in particular because there's private information. 00:16:33.220 --> 00:16:34.770 align:middle line:84% And if you're very close up, then 00:16:34.770 --> 00:16:36.545 align:middle line:84% essentially the lord sees everything. 00:16:36.545 --> 00:16:37.920 align:middle line:84% And if you're very far away, it's 00:16:37.920 --> 00:16:41.830 align:middle line:84% extremely costly and difficult for the lord to see everything. 00:16:41.830 --> 00:16:44.970 align:middle line:84% And so those exchanges have to be incentive, 00:16:44.970 --> 00:16:47.370 align:middle line:84% compatible, and induced, concepts 00:16:47.370 --> 00:16:49.260 align:middle line:90% we're going to define today. 00:16:49.260 --> 00:16:52.500 align:middle line:84% Or you may see nothing except with a cost where there's 00:16:52.500 --> 00:16:56.010 align:middle line:84% an audit, like a tax authority going in to actually take 00:16:56.010 --> 00:16:58.360 align:middle line:90% a close look, but at some cost. 00:16:58.360 --> 00:17:02.710 align:middle line:84% So here's the model for simplicity. 00:17:02.710 --> 00:17:05.450 align:middle line:84% Just imagine there are two agents, 00:17:05.450 --> 00:17:09.740 align:middle line:84% only one lord named agent 2 and one agent 00:17:09.740 --> 00:17:14.240 align:middle line:84% named agent 1 that's a stand-in for the entire villa 00:17:14.240 --> 00:17:15.329 align:middle line:90% population. 00:17:15.329 --> 00:17:18.710 align:middle line:84% So agent 1 here is seeing his or her endowment, 00:17:18.710 --> 00:17:20.569 align:middle line:84% 1 stands for the household number, 00:17:20.569 --> 00:17:23.810 align:middle line:84% epsilon for the fact that the endowments are 00:17:23.810 --> 00:17:27.349 align:middle line:84% the yields of crops grown on the land farmed by agent 1 00:17:27.349 --> 00:17:28.190 align:middle line:90% and a random. 00:17:28.190 --> 00:17:29.990 align:middle line:84% And furthermore, at least initially, 00:17:29.990 --> 00:17:32.840 align:middle line:90% only seen by agent 1, the villa. 00:17:32.840 --> 00:17:34.100 align:middle line:90% We can simplify. 00:17:34.100 --> 00:17:35.900 align:middle line:84% This notation was here deliberately 00:17:35.900 --> 00:17:37.760 align:middle line:84% to try to remind you a bit of things 00:17:37.760 --> 00:17:40.460 align:middle line:84% that we've done earlier in other lectures 00:17:40.460 --> 00:17:42.110 align:middle line:90% where epsilon was a shock. 00:17:42.110 --> 00:17:45.800 align:middle line:84% We talked about portfolios of land as a function of shocks, 00:17:45.800 --> 00:17:46.470 align:middle line:90% and so on. 00:17:46.470 --> 00:17:49.580 align:middle line:84% But in fact, this whole object can be just summarized 00:17:49.580 --> 00:17:53.330 align:middle line:84% by theta, a value lying in some sum 00:17:53.330 --> 00:17:57.590 align:middle line:84% set capital theta, occurring with realizations p of theta. 00:17:57.590 --> 00:18:00.860 align:middle line:84% Agent 2, the lord, we're going to simplify. 00:18:00.860 --> 00:18:04.190 align:middle line:84% The endowment is public, there's no private information there. 00:18:04.190 --> 00:18:06.680 align:middle line:84% Agent 2 is, again, the central monastery. 00:18:06.680 --> 00:18:10.700 align:middle line:84% Both these endowments, the e1 of epsilon, 00:18:10.700 --> 00:18:13.370 align:middle line:84% or theta on the one hand and W on the other, 00:18:13.370 --> 00:18:15.140 align:middle line:90% can be more than one crop. 00:18:15.140 --> 00:18:16.910 align:middle line:90% It can be multiple crops. 00:18:16.910 --> 00:18:20.340 align:middle line:84% So K is the dimension of the vector. 00:18:20.340 --> 00:18:21.710 align:middle line:90% So what do these guys do? 00:18:21.710 --> 00:18:26.970 align:middle line:84% The two agents agree to a plan, a resource allocation rule, 00:18:26.970 --> 00:18:31.070 align:middle line:84% which allows agent 1, the guy with the private information, 00:18:31.070 --> 00:18:35.090 align:middle line:84% to be sending messages to agent 2, 00:18:35.090 --> 00:18:40.940 align:middle line:84% and as a result of the message, some tax is paid from agent 1 00:18:40.940 --> 00:18:42.080 align:middle line:90% to agent 2. 00:18:42.080 --> 00:18:44.780 align:middle line:84% So little m is a particular message, 00:18:44.780 --> 00:18:48.080 align:middle line:84% big M here is the set of all possible messages 00:18:48.080 --> 00:18:49.580 align:middle line:90% or the message space. 00:18:49.580 --> 00:18:51.560 align:middle line:84% This is quite an abstract concept. 00:18:51.560 --> 00:18:55.250 align:middle line:84% It could be something like, it rained today, or, how's 00:18:55.250 --> 00:18:59.990 align:middle line:84% the weather over there, or, I lost my plow. 00:18:59.990 --> 00:19:02.090 align:middle line:90% This abstract message space. 00:19:02.090 --> 00:19:04.430 align:middle line:84% But we're going to give it some meaning. 00:19:04.430 --> 00:19:07.640 align:middle line:84% The meaning happens through this allocation rule. 00:19:07.640 --> 00:19:11.180 align:middle line:84% Namely, if theta is the true endowment 00:19:11.180 --> 00:19:14.330 align:middle line:84% of agent 1, how much of the tax, f, 00:19:14.330 --> 00:19:16.610 align:middle line:84% is a function of what is said, M. 00:19:16.610 --> 00:19:19.250 align:middle line:84% And they all agree to this abstract message space 00:19:19.250 --> 00:19:21.260 align:middle line:90% and to this allocation rule f. 00:19:21.260 --> 00:19:27.810 align:middle line:84% So agent 1 can map what he says into his overall outcome. 00:19:27.810 --> 00:19:31.070 align:middle line:84% So let's suppose the agent 1 knows exactly 00:19:31.070 --> 00:19:33.050 align:middle line:90% what he or she wants to do. 00:19:33.050 --> 00:19:36.230 align:middle line:84% Namely, when his or her endowment is theta. 00:19:36.230 --> 00:19:38.360 align:middle line:84% The best possible message that could 00:19:38.360 --> 00:19:42.470 align:middle line:84% be sent in that abstract space is, we'll put a star on, 00:19:42.470 --> 00:19:43.980 align:middle line:90% an m star of theta. 00:19:43.980 --> 00:19:48.320 align:middle line:84% This is the maximizing message sent by agent 1 to agent 2 00:19:48.320 --> 00:19:51.650 align:middle line:84% when his endowment is actually theta. 00:19:51.650 --> 00:19:55.430 align:middle line:84% This is way to write the fact that it's maximizing. 00:19:55.430 --> 00:20:00.290 align:middle line:84% Namely, the overall outcome for agent 1 in terms of agent 1's 00:20:00.290 --> 00:20:03.620 align:middle line:84% utility is as high as it can possibly 00:20:03.620 --> 00:20:07.190 align:middle line:84% be relative to any other possible message that 00:20:07.190 --> 00:20:08.450 align:middle line:90% could be sent. 00:20:08.450 --> 00:20:11.840 align:middle line:84% There may be ties, but at least m star is maximal. 00:20:11.840 --> 00:20:14.820 align:middle line:84% The inequality doesn't go the other way. 00:20:14.820 --> 00:20:16.820 align:middle line:84% If it went the other way, less than or equal to, 00:20:16.820 --> 00:20:19.190 align:middle line:84% there would be a message m that did better 00:20:19.190 --> 00:20:21.050 align:middle line:84% than what we said is the maximum, 00:20:21.050 --> 00:20:23.100 align:middle line:84% and that would be a contradiction. 00:20:23.100 --> 00:20:26.000 align:middle line:84% So 83 is just a statement of maximization. 00:20:26.000 --> 00:20:30.740 align:middle line:84% Now, this holds for any other possible message, little m. 00:20:30.740 --> 00:20:33.260 align:middle line:84% And in particular, if the reality 00:20:33.260 --> 00:20:37.640 align:middle line:84% had been something else, say theta tilde and not theta, 00:20:37.640 --> 00:20:41.390 align:middle line:84% m star would still denote the maximizing message, 00:20:41.390 --> 00:20:44.150 align:middle line:84% but it would maximize that theta tilde. 00:20:44.150 --> 00:20:46.190 align:middle line:84% The role that it plays here is that is 00:20:46.190 --> 00:20:51.170 align:middle line:84% a particular message like m, a particular counterfactual 00:20:51.170 --> 00:20:51.860 align:middle line:90% message. 00:20:51.860 --> 00:20:54.260 align:middle line:84% But because it's a valid message, 00:20:54.260 --> 00:20:57.320 align:middle line:84% although it would have been sent in different circumstances, 00:20:57.320 --> 00:20:59.900 align:middle line:84% we just can substitute m star of theta 00:20:59.900 --> 00:21:03.770 align:middle line:84% tilde up on the right-hand side as a particular m since 83 00:21:03.770 --> 00:21:06.200 align:middle line:84% holds for all possible m, and that 00:21:06.200 --> 00:21:08.930 align:middle line:90% gives us this expression 84. 00:21:08.930 --> 00:21:13.070 align:middle line:84% So the way to read this is that when the agent's true endowment 00:21:13.070 --> 00:21:15.690 align:middle line:84% is theta, see theta on both sides, 00:21:15.690 --> 00:21:19.400 align:middle line:84% and m star theta is maximal, that weakly dominates, 00:21:19.400 --> 00:21:23.750 align:middle line:84% saying what that actual dominates what the agent would 00:21:23.750 --> 00:21:26.720 align:middle line:84% have said in the counterfactual situation, where 00:21:26.720 --> 00:21:28.790 align:middle line:84% though his endowment were theta he could have 00:21:28.790 --> 00:21:32.420 align:middle line:90% said m star of theta tilde. 00:21:32.420 --> 00:21:33.392 align:middle line:90% With me so far? 00:21:33.392 --> 00:21:34.850 align:middle line:84% So these are just simple statements 00:21:34.850 --> 00:21:37.220 align:middle line:90% of maximization and notation. 00:21:37.220 --> 00:21:40.010 align:middle line:84% Now we're going to make a bigger move here, 00:21:40.010 --> 00:21:42.740 align:middle line:84% although it seems rather innocuous. 00:21:42.740 --> 00:21:44.900 align:middle line:84% We're going to change the message space 00:21:44.900 --> 00:21:47.450 align:middle line:84% and we're going to change the allocation rule. 00:21:47.450 --> 00:21:50.060 align:middle line:84% The way we're going to specialize the message space 00:21:50.060 --> 00:21:53.930 align:middle line:84% is to require that the agent announce values of theta. 00:21:53.930 --> 00:21:58.880 align:middle line:84% They're still not seen by the monastery agent 2, 00:21:58.880 --> 00:22:02.660 align:middle line:84% but the message space is my output was high this year, 00:22:02.660 --> 00:22:06.170 align:middle line:84% my output was low, et cetera, for as many possible values 00:22:06.170 --> 00:22:08.660 align:middle line:90% of endowment as there might be. 00:22:08.660 --> 00:22:10.590 align:middle line:90% So we change the message space. 00:22:10.590 --> 00:22:15.890 align:middle line:84% The next thing we do is change to transfer rule. 00:22:15.890 --> 00:22:19.970 align:middle line:84% Well, for one thing, we have to define the transfer rule 00:22:19.970 --> 00:22:22.500 align:middle line:90% over messages about theta. 00:22:22.500 --> 00:22:24.690 align:middle line:90% So we denote that g of theta. 00:22:24.690 --> 00:22:26.690 align:middle line:84% But actually, we're not going to, quote unquote, 00:22:26.690 --> 00:22:27.620 align:middle line:90% "change the rule." 00:22:27.620 --> 00:22:31.820 align:middle line:84% We're going to define g to be the same function f, 00:22:31.820 --> 00:22:34.940 align:middle line:84% but f used to operate on abstract messages 00:22:34.940 --> 00:22:39.590 align:middle line:84% whereas g operates on messages about the actual endowment. 00:22:39.590 --> 00:22:43.340 align:middle line:84% So the right-hand side here is a composite function. 00:22:43.340 --> 00:22:47.030 align:middle line:84% You have theta tilde, you send message m star of theta tilde, 00:22:47.030 --> 00:22:48.810 align:middle line:90% f acts on that. 00:22:48.810 --> 00:22:51.830 align:middle line:84% So it's a composition of f and m, 00:22:51.830 --> 00:22:55.940 align:middle line:84% whereas g operates directly on messages about output. 00:22:55.940 --> 00:22:57.720 align:middle line:84% There is another way to see this, 00:22:57.720 --> 00:23:00.620 align:middle line:84% which is where we're going in terms of the result. 00:23:00.620 --> 00:23:03.110 align:middle line:84% The agent knows the maximizing action 00:23:03.110 --> 00:23:05.130 align:middle line:90% for every possible theta. 00:23:05.130 --> 00:23:08.270 align:middle line:84% So he could program the computer to do 00:23:08.270 --> 00:23:11.420 align:middle line:84% what he wants it to do in terms of sending a message up 00:23:11.420 --> 00:23:14.250 align:middle line:90% to whatever key gets pushed. 00:23:14.250 --> 00:23:16.260 align:middle line:84% So effectively, he starts pushing 00:23:16.260 --> 00:23:20.370 align:middle line:84% keys that denote the theta, in this case, theta tilde, 00:23:20.370 --> 00:23:22.230 align:middle line:84% instead of actually sending a message. 00:23:22.230 --> 00:23:25.380 align:middle line:84% The computer sends the message on behalf of the agent. 00:23:25.380 --> 00:23:29.290 align:middle line:84% Of course, the agent has, a 1, has coded it all up. 00:23:29.290 --> 00:23:33.030 align:middle line:84% So the computer functions properly 00:23:33.030 --> 00:23:35.670 align:middle line:84% on behalf of the agent's best interests. 00:23:35.670 --> 00:23:36.450 align:middle line:90% All right. 00:23:36.450 --> 00:23:39.390 align:middle line:84% So now we've changed two things, the message space 00:23:39.390 --> 00:23:41.580 align:middle line:90% and the allocation rule. 00:23:41.580 --> 00:23:47.390 align:middle line:84% And now we go back to previously derived equation, 84, 00:23:47.390 --> 00:23:52.450 align:middle line:84% that said this thing, but start substituting-- 00:23:52.450 --> 00:23:55.930 align:middle line:84% m star of theta tilde is composed 00:23:55.930 --> 00:24:00.100 align:middle line:84% with f will be g of theta tilde on the left-hand side, 00:24:00.100 --> 00:24:04.210 align:middle line:84% f composed with m star of theta will be g of theta 00:24:04.210 --> 00:24:08.140 align:middle line:90% just by the definition of g. 00:24:08.140 --> 00:24:09.100 align:middle line:90% So we get this. 00:24:09.100 --> 00:24:11.070 align:middle line:90% We get 85. 00:24:11.070 --> 00:24:13.080 align:middle line:90% That's just substitution. 00:24:13.080 --> 00:24:15.000 align:middle line:90% But it's powerful. 00:24:15.000 --> 00:24:15.660 align:middle line:90% OK? 00:24:15.660 --> 00:24:20.160 align:middle line:84% So now we can start calling it, misleadingly, 00:24:20.160 --> 00:24:21.810 align:middle line:90% a truth-telling constraint. 00:24:21.810 --> 00:24:23.910 align:middle line:84% Now, no one is choking this guy to death. 00:24:23.910 --> 00:24:27.190 align:middle line:84% He gets to say whatever he wants. 00:24:27.190 --> 00:24:31.710 align:middle line:84% But under this new message space with the g allocation rule, 00:24:31.710 --> 00:24:35.070 align:middle line:84% when theta actually happens, he wants 00:24:35.070 --> 00:24:38.490 align:middle line:84% to say it did, as opposed to when theta actually 00:24:38.490 --> 00:24:42.210 align:middle line:84% happens, lying and saying that it's theta tilde. 00:24:42.210 --> 00:24:45.590 align:middle line:84% So this constraint 85, which was actually derived just 00:24:45.590 --> 00:24:47.810 align:middle line:84% from a principle of maximization, 00:24:47.810 --> 00:24:51.650 align:middle line:84% actually starts looking like a truth-telling constraint, where 00:24:51.650 --> 00:24:56.000 align:middle line:84% the space of messages is the space of possible outputs, 00:24:56.000 --> 00:24:58.250 align:middle line:84% and now miraculously, the agent's 00:24:58.250 --> 00:25:01.040 align:middle line:84% going to tell the monastery the truth about it. 00:25:01.040 --> 00:25:03.960 align:middle line:84% The bill is going to tell the monastery the truth about it. 00:25:03.960 --> 00:25:06.800 align:middle line:84% But we're not kind of insisting on truth telling. 00:25:06.800 --> 00:25:10.460 align:middle line:84% 85 is derived as a first principle. 00:25:10.460 --> 00:25:14.140 align:middle line:84% They're called incentive compatibility constraints. 00:25:14.140 --> 00:25:16.060 align:middle line:84% Anyway, so once this mechanism is 00:25:16.060 --> 00:25:18.560 align:middle line:84% in place, whenever theta happens, 00:25:18.560 --> 00:25:21.640 align:middle line:84% the agent will say so, affecting g. 00:25:21.640 --> 00:25:24.100 align:middle line:84% The g is actually what would have happened 00:25:24.100 --> 00:25:26.650 align:middle line:84% under the old mechanism when theta happens 00:25:26.650 --> 00:25:30.890 align:middle line:84% and the agent announced m star of theta in the abstract space. 00:25:30.890 --> 00:25:35.590 align:middle line:84% So this is now achieving exactly the same set of allocations. 00:25:35.590 --> 00:25:38.830 align:middle line:84% In fact, we could call them shock contingent allocations. 00:25:38.830 --> 00:25:42.670 align:middle line:84% If you go back to the very early notation 00:25:42.670 --> 00:25:44.830 align:middle line:84% with the shock in there, it looks 00:25:44.830 --> 00:25:48.740 align:middle line:84% like the agent is announcing what those shocks are, 00:25:48.740 --> 00:25:51.610 align:middle line:84% and under this allocation rule, will 00:25:51.610 --> 00:25:54.340 align:middle line:84% be telling the truth about them as long as 85 00:25:54.340 --> 00:25:56.840 align:middle line:90% is part of the system. 00:25:56.840 --> 00:26:00.500 align:middle line:84% So just like before when we had states of the world, 00:26:00.500 --> 00:26:04.240 align:middle line:84% we talked about state contingent allocations, like gift giving, 00:26:04.240 --> 00:26:06.910 align:middle line:84% the risk sharing rules, and so on, here, again, we're 00:26:06.910 --> 00:26:10.040 align:middle line:84% enumerating these states, epsilon in this case, 00:26:10.040 --> 00:26:13.280 align:middle line:84% when we talk about state contingent allocations. 00:26:13.280 --> 00:26:15.250 align:middle line:84% So the method is exactly the same 00:26:15.250 --> 00:26:18.760 align:middle line:84% as before as long as we append onto the system 00:26:18.760 --> 00:26:20.890 align:middle line:90% constraints like 85. 00:26:20.890 --> 00:26:24.010 align:middle line:84% Another way to say that is all of the consequences 00:26:24.010 --> 00:26:27.130 align:middle line:84% of private information are captured by 85. 00:26:27.130 --> 00:26:30.970 align:middle line:84% So we can go and do our thing with the programming problems, 00:26:30.970 --> 00:26:33.820 align:middle line:84% maximizing lambda weighted sums of utilities 00:26:33.820 --> 00:26:37.750 align:middle line:84% subject to resource constraints, and so on, and just 00:26:37.750 --> 00:26:42.410 align:middle line:84% append on these extra so-called truth-telling constraints. 00:26:42.410 --> 00:26:46.060 align:middle line:84% So we don't have to search over abstract message spaces, 00:26:46.060 --> 00:26:48.310 align:middle line:84% because what's the limit of that? 00:26:48.310 --> 00:26:50.650 align:middle line:84% Anybody can come up with a message space. 00:26:50.650 --> 00:26:53.930 align:middle line:84% It's too abstract and not very specific. 00:26:53.930 --> 00:26:58.570 align:middle line:84% We restrict the message space, but without loss of generality. 00:26:58.570 --> 00:27:01.720 align:middle line:84% And anything we could have done in an abstract way 00:27:01.720 --> 00:27:04.300 align:middle line:84% with m and f, we can now do with theta and g. 00:27:04.300 --> 00:27:07.010 align:middle line:90% 00:27:07.010 --> 00:27:10.400 align:middle line:84% So here, in fact, would be a programming problem. 00:27:10.400 --> 00:27:13.100 align:middle line:84% We're going to maximize the lambda-weighted sums 00:27:13.100 --> 00:27:14.090 align:middle line:90% of utilities. 00:27:14.090 --> 00:27:16.550 align:middle line:84% A little bit of new notation, I guess, 00:27:16.550 --> 00:27:18.380 align:middle line:90% if I forgot to say it earlier. 00:27:18.380 --> 00:27:21.360 align:middle line:84% Theta occurs with probability P of theta. 00:27:21.360 --> 00:27:25.040 align:middle line:84% So summing over theta makes this an expected utility 00:27:25.040 --> 00:27:28.070 align:middle line:84% representation on the left-hand side. 00:27:28.070 --> 00:27:30.050 align:middle line:84% Note that what the agent gives up, 00:27:30.050 --> 00:27:34.460 align:middle line:84% minus g, is what the monastery gets, plus g. 00:27:34.460 --> 00:27:37.970 align:middle line:84% There is an expected utility term for the monastery, too. 00:27:37.970 --> 00:27:40.100 align:middle line:90% This is a two-party contract. 00:27:40.100 --> 00:27:41.930 align:middle line:84% They're going to maximize this thing. 00:27:41.930 --> 00:27:45.170 align:middle line:84% We are going to maximize it for them to determine 00:27:45.170 --> 00:27:48.860 align:middle line:84% Pareto-optimal allocations and make a prediction about what 00:27:48.860 --> 00:27:52.550 align:middle line:84% they would be doing, subject to this extra constraint-- 00:27:52.550 --> 00:27:56.500 align:middle line:84% 87, the so-called truth-telling constraint. 00:27:56.500 --> 00:27:58.990 align:middle line:84% You may say, well, where is the resource constraint? 00:27:58.990 --> 00:28:02.200 align:middle line:84% Well, it kind of got substituted in to the objective function 00:28:02.200 --> 00:28:05.650 align:middle line:84% because what agent 1 gives up is what agent 2 gets. 00:28:05.650 --> 00:28:09.190 align:middle line:84% So there's no reason to talk about consumption of agent 1 00:28:09.190 --> 00:28:11.080 align:middle line:84% and consumption of agent 2, and make sure 00:28:11.080 --> 00:28:13.100 align:middle line:90% that it adds up to the total. 00:28:13.100 --> 00:28:18.070 align:middle line:84% That's just a handy convenience in this setup. 00:28:18.070 --> 00:28:21.430 align:middle line:90% So more ways to implement it-- 00:28:21.430 --> 00:28:23.900 align:middle line:84% the villa is, at the end of the year-- 00:28:23.900 --> 00:28:26.620 align:middle line:84% and so far, this is a static problem-- 00:28:26.620 --> 00:28:29.980 align:middle line:84% the agent just hands over goods to the monastery. 00:28:29.980 --> 00:28:31.840 align:middle line:84% Could be a lot, could be a little-- whatever 00:28:31.840 --> 00:28:33.700 align:middle line:90% it is, it's totally accepted. 00:28:33.700 --> 00:28:37.390 align:middle line:84% As a solution to this problem, instead of saying, 00:28:37.390 --> 00:28:40.690 align:middle line:84% oh, I'm announcing theta and I'm going to give you g of theta, 00:28:40.690 --> 00:28:42.460 align:middle line:90% they just hand it over. 00:28:42.460 --> 00:28:43.710 align:middle line:90% It's the same thing. 00:28:43.710 --> 00:28:45.250 align:middle line:90% It's just simpler. 00:28:45.250 --> 00:28:48.680 align:middle line:84% Now the key is, again, this incentive constraint, 00:28:48.680 --> 00:28:51.940 align:middle line:84% which makes sure that agent 1 has the incentive 00:28:51.940 --> 00:28:54.580 align:middle line:84% to hand over the right amount, the right amount being 00:28:54.580 --> 00:28:58.070 align:middle line:84% the solution to this programming problem. 00:28:58.070 --> 00:29:02.530 align:middle line:84% Second consequence-- suppose there's only one good, wheat. 00:29:02.530 --> 00:29:06.410 align:middle line:84% When you look at 87, it's going to simplify to something 00:29:06.410 --> 00:29:09.200 align:middle line:90% trivial, namely, no trade. 00:29:09.200 --> 00:29:10.370 align:middle line:90% Why is that? 00:29:10.370 --> 00:29:12.890 align:middle line:84% This says utility on the left weakly 00:29:12.890 --> 00:29:15.080 align:middle line:90% exceeds utility on the right. 00:29:15.080 --> 00:29:20.030 align:middle line:84% And g of theta on the left must be less than or equal to g 00:29:20.030 --> 00:29:23.280 align:middle line:84% of theta tilde on the right because it's the same function 00:29:23.280 --> 00:29:23.780 align:middle line:90% u. 00:29:23.780 --> 00:29:26.000 align:middle line:84% And theta is the same argument otherwise. 00:29:26.000 --> 00:29:29.150 align:middle line:84% But you can reverse the logic, and put theta tilde 00:29:29.150 --> 00:29:31.730 align:middle line:84% for the actual situation and theta 00:29:31.730 --> 00:29:34.070 align:middle line:84% for the counterfactual situation. 00:29:34.070 --> 00:29:37.040 align:middle line:84% You'll get another inequality because this holds 00:29:37.040 --> 00:29:39.245 align:middle line:90% for all theta and theta tilde. 00:29:39.245 --> 00:29:41.120 align:middle line:84% And then you're going to have the consequence 00:29:41.120 --> 00:29:43.730 align:middle line:84% that g of theta tilde on the left must be less than 00:29:43.730 --> 00:29:46.250 align:middle line:84% or equal to g of theta on the right. 00:29:46.250 --> 00:29:48.898 align:middle line:84% Now we've got two inequalities-- less than or equal to, 00:29:48.898 --> 00:29:49.940 align:middle line:90% greater than or equal to. 00:29:49.940 --> 00:29:50.990 align:middle line:90% It must be equal to. 00:29:50.990 --> 00:29:53.940 align:middle line:84% So g is the same regardless of theta. 00:29:53.940 --> 00:29:56.720 align:middle line:84% So at most, the villa is paying over 00:29:56.720 --> 00:29:59.180 align:middle line:90% to the monastery a constant tax. 00:29:59.180 --> 00:30:01.250 align:middle line:84% But then it's not state contingent, 00:30:01.250 --> 00:30:05.430 align:middle line:84% and it could be 0 if we wanted to make them both better off. 00:30:05.430 --> 00:30:09.350 align:middle line:84% So that degeneration does not necessarily 00:30:09.350 --> 00:30:11.810 align:middle line:84% happen if there's more than one good. 00:30:11.810 --> 00:30:15.500 align:middle line:84% And it could be another good is like labor, not just wheat. 00:30:15.500 --> 00:30:18.800 align:middle line:84% And the specification is, you've got to go, 00:30:18.800 --> 00:30:20.300 align:middle line:90% here's the transfer of wheat. 00:30:20.300 --> 00:30:23.300 align:middle line:84% And otherwise, I'm going to go work for you 00:30:23.300 --> 00:30:25.910 align:middle line:84% on the land in my village, or trundle off 00:30:25.910 --> 00:30:28.050 align:middle line:90% to the monastery to work there. 00:30:28.050 --> 00:30:31.520 align:middle line:84% So there could be a wheat/labor trade-off, 00:30:31.520 --> 00:30:34.700 align:middle line:84% as an example of more than one good. 00:30:34.700 --> 00:30:37.040 align:middle line:90% And then this is not trivial. 00:30:37.040 --> 00:30:39.330 align:middle line:90% And some trade is possible. 00:30:39.330 --> 00:30:43.280 align:middle line:84% Another special case-- if agent 1 00:30:43.280 --> 00:30:47.240 align:middle line:84% is risk averse in a certain way, then we 00:30:47.240 --> 00:30:51.740 align:middle line:84% may be able to get some trade even if there's only one good. 00:30:51.740 --> 00:30:54.650 align:middle line:84% So this is just going to exploit the possibility 00:30:54.650 --> 00:30:58.170 align:middle line:84% that if agent 1 has a strictly concave utility function, 00:30:58.170 --> 00:31:02.270 align:middle line:84% then the degree of it will determine his or her adversity 00:31:02.270 --> 00:31:03.260 align:middle line:90% to lotteries. 00:31:03.260 --> 00:31:07.890 align:middle line:84% So for example, you might say I'm high today. 00:31:07.890 --> 00:31:09.650 align:middle line:84% I would pay a big tax, but I'm going 00:31:09.650 --> 00:31:12.980 align:middle line:84% to pretend that I'm low so that I pay less of a tax. 00:31:12.980 --> 00:31:15.830 align:middle line:84% But that claim of having a low value 00:31:15.830 --> 00:31:18.230 align:middle line:90% may make the tax very random. 00:31:18.230 --> 00:31:22.010 align:middle line:84% And if he's really high, and that being a high value 00:31:22.010 --> 00:31:24.890 align:middle line:84% makes the guy very risk averse for odd reasons, 00:31:24.890 --> 00:31:26.780 align:middle line:84% then he may not want to claim low 00:31:26.780 --> 00:31:30.560 align:middle line:84% because he prefers to avoid the randomness associated 00:31:30.560 --> 00:31:32.170 align:middle line:90% with the lotteries. 00:31:32.170 --> 00:31:34.060 align:middle line:84% So lotteries in general are going 00:31:34.060 --> 00:31:37.120 align:middle line:84% to help sustain trade because they exploit 00:31:37.120 --> 00:31:39.950 align:middle line:90% differentiable risk aversion. 00:31:39.950 --> 00:31:44.170 align:middle line:84% So with that said, we can now write this program up here 00:31:44.170 --> 00:31:45.730 align:middle line:90% in lotteries. 00:31:45.730 --> 00:31:48.940 align:middle line:84% Let's call pi of tau given theta the probability 00:31:48.940 --> 00:31:54.070 align:middle line:84% of a transfer from agent 1 to agent 2 of magnitude tau, 00:31:54.070 --> 00:31:56.480 align:middle line:84% conditioned on the agent saying theta. 00:31:56.480 --> 00:32:00.040 align:middle line:84% And then this program 6 over here becomes 7, 00:32:00.040 --> 00:32:04.570 align:middle line:84% where we're still maximizing a weighted sum of utilities 00:32:04.570 --> 00:32:07.720 align:middle line:84% subject to an implicit resource constraint. 00:32:07.720 --> 00:32:09.400 align:middle line:84% What one guy gives up, the other guy 00:32:09.400 --> 00:32:15.070 align:middle line:84% gets, in the tau, but also this now-revised incentive 00:32:15.070 --> 00:32:16.520 align:middle line:90% constraint. 00:32:16.520 --> 00:32:18.040 align:middle line:90% And let me read it for you-- 00:32:18.040 --> 00:32:21.640 align:middle line:84% when theta comes up, that's the actual yield. 00:32:21.640 --> 00:32:24.400 align:middle line:84% Agent 1 says, Yep, that's my theta. 00:32:24.400 --> 00:32:27.640 align:middle line:84% That's the message, tells the truth about it. 00:32:27.640 --> 00:32:32.620 align:middle line:84% That implements a lottery with probabilities pi of tau 00:32:32.620 --> 00:32:35.770 align:middle line:84% so that summing over all the tau gives the expected utility 00:32:35.770 --> 00:32:39.350 align:middle line:84% of the agent for having theta and telling the truth about it. 00:32:39.350 --> 00:32:42.430 align:middle line:84% And on the right-hand side is the counterfactual 00:32:42.430 --> 00:32:45.200 align:middle line:84% that although theta came up, he lies, and says, 00:32:45.200 --> 00:32:47.950 align:middle line:90% nope, I'm theta tilde. 00:32:47.950 --> 00:32:51.250 align:middle line:84% But that comes with this potential randomness, 00:32:51.250 --> 00:32:54.070 align:middle line:84% and the expected utility on the right-hand side 00:32:54.070 --> 00:32:57.910 align:middle line:84% is not greater than it is on the left. 00:32:57.910 --> 00:33:01.320 align:middle line:84% So that's the same kind of truth telling incentive compatibility 00:33:01.320 --> 00:33:05.160 align:middle line:84% constraint as before, with the simple addition that we 00:33:05.160 --> 00:33:08.030 align:middle line:90% have those lotteries in there. 00:33:08.030 --> 00:33:11.180 align:middle line:84% You will recognize, because we've done this before, 00:33:11.180 --> 00:33:15.600 align:middle line:84% that with the lotteries, things turn into linear programs. 00:33:15.600 --> 00:33:18.410 align:middle line:84% So when you look at this, the control variables 00:33:18.410 --> 00:33:22.280 align:middle line:84% are these pi of taus, and in the objective function, 00:33:22.280 --> 00:33:26.760 align:middle line:84% they're multiplied by these leading coefficients. 00:33:26.760 --> 00:33:30.540 align:middle line:84% And in the constraint set, the control variables 00:33:30.540 --> 00:33:33.510 align:middle line:84% are, again, the pi of taus weighted 00:33:33.510 --> 00:33:35.560 align:middle line:90% by certain coefficients. 00:33:35.560 --> 00:33:38.910 align:middle line:84% So I won't repeat what we talked about that day when 00:33:38.910 --> 00:33:40.830 align:middle line:90% we introduced this concept. 00:33:40.830 --> 00:33:43.140 align:middle line:84% I'm really just trying to remind you 00:33:43.140 --> 00:33:45.660 align:middle line:84% that we've already seen things like this, 00:33:45.660 --> 00:33:48.720 align:middle line:84% except that here, we have added the addition 00:33:48.720 --> 00:33:52.140 align:middle line:84% of these so-called truth-telling or incentive compatibility 00:33:52.140 --> 00:33:55.290 align:middle line:84% constraints, also written down in lotteries. 00:33:55.290 --> 00:33:57.990 align:middle line:84% And because it's a linear programming problem, 00:33:57.990 --> 00:34:01.590 align:middle line:84% we can compute solutions to it, which you've 00:34:01.590 --> 00:34:04.020 align:middle line:84% been doing on some of your homework problems, 00:34:04.020 --> 00:34:08.110 align:middle line:84% not with lotteries per se, but computing. 00:34:08.110 --> 00:34:12.159 align:middle line:84% Now, there is another twist here in terms of incentives. 00:34:12.159 --> 00:34:16.540 align:middle line:84% If it's true, say, that high-theta guys might 00:34:16.540 --> 00:34:20.170 align:middle line:84% want to claim to be low because they would pay less of a tax, 00:34:20.170 --> 00:34:23.409 align:middle line:84% I should say, where is that intuition coming from? 00:34:23.409 --> 00:34:27.250 align:middle line:84% If agent 1 is risk averse and agent 2 is risk neutral, 00:34:27.250 --> 00:34:30.880 align:middle line:84% then agent 2 should bear all the risk, in which case 00:34:30.880 --> 00:34:33.670 align:middle line:84% when agent 1 has a high value of theta, 00:34:33.670 --> 00:34:36.730 align:middle line:90% he would transfer stuff to 2. 00:34:36.730 --> 00:34:39.040 align:middle line:84% And likewise, if agent 1 has a low value of theta, 00:34:39.040 --> 00:34:42.040 align:middle line:84% he would receive stuff from 2, and consumption 00:34:42.040 --> 00:34:44.170 align:middle line:84% would be constant if it weren't for these incentive 00:34:44.170 --> 00:34:45.280 align:middle line:90% constraints. 00:34:45.280 --> 00:34:48.909 align:middle line:84% But agent 2 doesn't have to be risk neutral. 00:34:48.909 --> 00:34:51.880 align:middle line:84% They could both be strictly concave people. 00:34:51.880 --> 00:34:54.850 align:middle line:84% We still know that apart from 94, 00:34:54.850 --> 00:34:59.140 align:middle line:84% there is this monotonicity condition, that consumptions 00:34:59.140 --> 00:35:00.950 align:middle line:90% should co-move together. 00:35:00.950 --> 00:35:05.920 align:middle line:84% So when theta is high, agent 1's consumption could go up. 00:35:05.920 --> 00:35:08.260 align:middle line:84% But so also should agent 2, meaning 00:35:08.260 --> 00:35:12.730 align:middle line:84% that some of that high value is being transferred to agent 2. 00:35:12.730 --> 00:35:16.480 align:middle line:84% So it's the same whether or not 2 is risk neutral or not. 00:35:16.480 --> 00:35:20.800 align:middle line:84% Now, that intuition when the endowment is high, 00:35:20.800 --> 00:35:23.770 align:middle line:84% agent 1 could claim that it is low in order 00:35:23.770 --> 00:35:26.140 align:middle line:90% to avoid paying this transfer. 00:35:26.140 --> 00:35:29.380 align:middle line:84% But there is a way to preventing him from doing that. 00:35:29.380 --> 00:35:33.100 align:middle line:84% It's like-- I don't know, I'm not a gambler myself-- 00:35:33.100 --> 00:35:35.650 align:middle line:84% like when they call you, they put it on the table, 00:35:35.650 --> 00:35:37.510 align:middle line:90% and say, let me see your hand. 00:35:37.510 --> 00:35:41.260 align:middle line:84% So they say, OK, you're claiming you're low. 00:35:41.260 --> 00:35:46.250 align:middle line:84% Actually, let me apologize-- this goes the other way. 00:35:46.250 --> 00:35:50.005 align:middle line:84% You only need to worry about high guys claiming to be low. 00:35:50.005 --> 00:35:52.270 align:middle line:84% Low guys cannot claim to be high. 00:35:52.270 --> 00:35:53.290 align:middle line:90% Why? 00:35:53.290 --> 00:35:56.950 align:middle line:84% Because if they claim to be high without necessarily taking it 00:35:56.950 --> 00:35:59.320 align:middle line:84% away, they have to display their wealth. 00:35:59.320 --> 00:36:03.010 align:middle line:84% And then it would be clear, if they can't do it, 00:36:03.010 --> 00:36:04.880 align:middle line:90% that they were lying. 00:36:04.880 --> 00:36:07.820 align:middle line:84% So we kind of have a one-way incentive constraint going on 00:36:07.820 --> 00:36:09.440 align:middle line:90% here. 00:36:09.440 --> 00:36:12.410 align:middle line:84% That's not terribly important, but the show and tell 00:36:12.410 --> 00:36:14.780 align:middle line:90% is a device that can be used. 00:36:14.780 --> 00:36:16.830 align:middle line:90% And we'll come back to it later. 00:36:16.830 --> 00:36:20.360 align:middle line:84% All right, so now let's get into multiple periods, 00:36:20.360 --> 00:36:23.600 align:middle line:84% be a little bit more realistic about this, just slightly-- 00:36:23.600 --> 00:36:26.030 align:middle line:90% two periods rather than one. 00:36:26.030 --> 00:36:30.320 align:middle line:84% Same actors-- agent 1 having these random endowments 00:36:30.320 --> 00:36:34.760 align:middle line:84% in both periods, agent 2 having a potential time-varying 00:36:34.760 --> 00:36:38.450 align:middle line:84% endowment W. And then these probabilities of shocks, 00:36:38.450 --> 00:36:41.240 align:middle line:84% theta 2 to agent 1 in the second period, 00:36:41.240 --> 00:36:44.840 align:middle line:84% are basically potentially non-independent they 00:36:44.840 --> 00:36:50.030 align:middle line:84% could be determined by the shock that agent 1 incurs at date 1. 00:36:50.030 --> 00:36:51.410 align:middle line:84% So if you're into statistics, you 00:36:51.410 --> 00:36:54.510 align:middle line:84% could call this a Markov process and be fancy about it, 00:36:54.510 --> 00:36:56.390 align:middle line:84% but all you really need to know is 00:36:56.390 --> 00:36:58.710 align:middle line:90% the state-dependent notation. 00:36:58.710 --> 00:37:01.490 align:middle line:84% OK, so I want to know what's an optimal arrangement 00:37:01.490 --> 00:37:02.670 align:middle line:90% in this world. 00:37:02.670 --> 00:37:06.510 align:middle line:84% So we write down the maximization problem, 00:37:06.510 --> 00:37:09.650 align:middle line:84% which is the lambda-weighted sum of expected utilities, 00:37:09.650 --> 00:37:12.770 align:middle line:84% obviously taking into account both periods 00:37:12.770 --> 00:37:16.970 align:middle line:84% subject to resource constraints and to incentive compatibility 00:37:16.970 --> 00:37:18.180 align:middle line:90% constraints. 00:37:18.180 --> 00:37:21.290 align:middle line:84% So there's a lot of lines here, unfortunately, 00:37:21.290 --> 00:37:23.060 align:middle line:90% but it's not so bad. 00:37:23.060 --> 00:37:27.470 align:middle line:84% This is lambda 1 weight for agent 1, 00:37:27.470 --> 00:37:29.840 align:middle line:90% lambda 2 weight for agent 2. 00:37:29.840 --> 00:37:35.360 align:middle line:84% Otherwise, this is the first period expected utility 00:37:35.360 --> 00:37:38.240 align:middle line:84% when the agent is theta 1 and says so, 00:37:38.240 --> 00:37:40.310 align:middle line:90% affecting the transfer tau. 00:37:40.310 --> 00:37:43.310 align:middle line:84% This new term here is beta, discount rate, 00:37:43.310 --> 00:37:47.210 align:middle line:84% times the expected utility in period 2. 00:37:47.210 --> 00:37:49.700 align:middle line:90% Period 2, agent 1 has theta 2-- 00:37:49.700 --> 00:37:51.230 align:middle line:90% actually says so. 00:37:51.230 --> 00:37:54.560 align:middle line:84% And then you integrate up over all possible thetas 00:37:54.560 --> 00:37:56.150 align:middle line:90% and discount it by beta. 00:37:56.150 --> 00:37:58.700 align:middle line:84% One little subtlety I'm about to feature 00:37:58.700 --> 00:38:02.270 align:middle line:84% is the transfers at day 2 can depend not only 00:38:02.270 --> 00:38:04.640 align:middle line:84% on what is said about theta 2, but what 00:38:04.640 --> 00:38:07.220 align:middle line:90% was said about theta 1-- 00:38:07.220 --> 00:38:09.410 align:middle line:84% the history, as it were-- in date 1. 00:38:09.410 --> 00:38:10.568 align:middle line:90% Date 1 is the first day. 00:38:10.568 --> 00:38:11.360 align:middle line:90% Nothing's happened. 00:38:11.360 --> 00:38:13.370 align:middle line:84% There's no history, but there is a history 00:38:13.370 --> 00:38:16.490 align:middle line:90% to potentially use at day 2. 00:38:16.490 --> 00:38:18.690 align:middle line:84% So this is the objective function. 00:38:18.690 --> 00:38:20.240 align:middle line:84% And again, the resource constraints 00:38:20.240 --> 00:38:23.150 align:middle line:84% are loaded in here because what agent 1 gives up, 00:38:23.150 --> 00:38:24.560 align:middle line:90% agent 2 is getting. 00:38:24.560 --> 00:38:27.110 align:middle line:84% So we don't need to worry about that, for both dates 00:38:27.110 --> 00:38:29.120 align:middle line:84% and whatever the outcome of the lottery. 00:38:29.120 --> 00:38:32.900 align:middle line:84% Now, let's think about the incentive constraints, 00:38:32.900 --> 00:38:36.080 align:middle line:84% working backwards, as in dynamic programming, 00:38:36.080 --> 00:38:37.530 align:middle line:90% from the last period. 00:38:37.530 --> 00:38:41.930 align:middle line:84% So say some theta 1 were already announced, and that's history. 00:38:41.930 --> 00:38:44.120 align:middle line:90% They arrive at day 2. 00:38:44.120 --> 00:38:47.750 align:middle line:84% Agent 2 has a choice about saying the actual value 00:38:47.750 --> 00:38:53.150 align:middle line:84% of theta, theta sub 2, telling the truth, or lying about it, 00:38:53.150 --> 00:38:55.320 align:middle line:90% and saying theta 2 tilde. 00:38:55.320 --> 00:38:58.310 align:middle line:84% So what does that incentive constraint look like? 00:38:58.310 --> 00:39:01.880 align:middle line:84% We're already in the last date, so there's one period left. 00:39:01.880 --> 00:39:03.590 align:middle line:90% It's period 2. 00:39:03.590 --> 00:39:08.450 align:middle line:84% And this is got theta 2, say so, versus got theta 2 00:39:08.450 --> 00:39:10.970 align:middle line:84% and lie about it, saying theta tilde. 00:39:10.970 --> 00:39:15.080 align:middle line:84% This history, theta 1, is the past in the archives. 00:39:15.080 --> 00:39:19.010 align:middle line:84% So it's in both sides because that's already public record-- 00:39:19.010 --> 00:39:22.670 align:middle line:84% not what theta 1 was per se, but that it was announced, 00:39:22.670 --> 00:39:23.840 align:middle line:90% theta tilde. 00:39:23.840 --> 00:39:26.810 align:middle line:84% Now the incentive constrain at day 1, 00:39:26.810 --> 00:39:30.170 align:middle line:84% working backwards from day 2, looks a little bit more 00:39:30.170 --> 00:39:31.230 align:middle line:90% complicated. 00:39:31.230 --> 00:39:35.598 align:middle line:84% But it's just going to use what we already know from 96-- 00:39:35.598 --> 00:39:37.640 align:middle line:84% that they will tell the truth in the second date, 00:39:37.640 --> 00:39:39.830 align:middle line:84% regardless of whatever history was 00:39:39.830 --> 00:39:41.600 align:middle line:90% announced in the first date. 00:39:41.600 --> 00:39:44.240 align:middle line:84% So these branches here, with the beta 00:39:44.240 --> 00:39:49.160 align:middle line:84% in front of it on both sides, are here, have theta 2, 00:39:49.160 --> 00:39:55.550 align:middle line:84% say theta 2 truthfully, versus have theta 2, and say theta 2 00:39:55.550 --> 00:39:56.450 align:middle line:90% truthfully. 00:39:56.450 --> 00:39:58.820 align:middle line:84% So on both the left and the right-hand side, 00:39:58.820 --> 00:40:01.070 align:middle line:84% the second period is not in doubt. 00:40:01.070 --> 00:40:05.000 align:middle line:84% The agent is going to be telling the truth because of 96. 00:40:05.000 --> 00:40:07.910 align:middle line:84% The real action has to do with the first term 00:40:07.910 --> 00:40:11.000 align:middle line:84% of the first date, namely have theta 1 00:40:11.000 --> 00:40:14.240 align:middle line:84% and say so versus have theta 1 and lie about it, 00:40:14.240 --> 00:40:16.280 align:middle line:90% and say theta 1 tilde. 00:40:16.280 --> 00:40:18.920 align:middle line:84% And this inequality constraint means 00:40:18.920 --> 00:40:22.820 align:middle line:84% that a weakly dominant strategy is to tell the truth-- 00:40:22.820 --> 00:40:25.430 align:middle line:90% have theta 1, say so. 00:40:25.430 --> 00:40:28.010 align:middle line:84% Now note, again, the interesting way 00:40:28.010 --> 00:40:30.620 align:middle line:90% in which this history evolves. 00:40:30.620 --> 00:40:34.940 align:middle line:84% If they say theta 1, it will be part of the history of day 2. 00:40:34.940 --> 00:40:38.990 align:middle line:84% They could say-- they won't-- but they could have said theta 00:40:38.990 --> 00:40:41.300 align:middle line:90% 1 tilde and lied about it. 00:40:41.300 --> 00:40:45.150 align:middle line:84% And that would also be recorded on the books as history. 00:40:45.150 --> 00:40:47.660 align:middle line:84% So the thing that's varying at the second date 00:40:47.660 --> 00:40:49.640 align:middle line:84% is this announcement in the first date, 00:40:49.640 --> 00:40:53.210 align:middle line:84% as we consider logically what the agent will 00:40:53.210 --> 00:40:55.190 align:middle line:90% want to say in the first date. 00:40:55.190 --> 00:40:57.870 align:middle line:84% So this is another incentive constraint. 00:40:57.870 --> 00:41:00.090 align:middle line:84% And again, there's more than one of them. 00:41:00.090 --> 00:41:03.170 align:middle line:84% This is for every possible actual theta 1. 00:41:03.170 --> 00:41:08.540 align:middle line:84% In any potential counterfactual announcement theta 1 tilde, 00:41:08.540 --> 00:41:10.160 align:middle line:90% constraint like this holds. 00:41:10.160 --> 00:41:12.350 align:middle line:84% So I should have caught myself earlier on this, 00:41:12.350 --> 00:41:14.720 align:middle line:84% because I talked about the incentive 00:41:14.720 --> 00:41:17.780 align:middle line:84% constraint or the truth-telling constraint 00:41:17.780 --> 00:41:20.030 align:middle line:90% as if there were only one. 00:41:20.030 --> 00:41:22.520 align:middle line:84% But in practice, there are many because we 00:41:22.520 --> 00:41:25.800 align:middle line:84% have many possible realizations of theta. 00:41:25.800 --> 00:41:29.450 align:middle line:84% So what we've done today so far is called the "revelation 00:41:29.450 --> 00:41:32.570 align:middle line:84% principle," meaning that those truth-telling constraints can 00:41:32.570 --> 00:41:35.960 align:middle line:84% be imposed without any loss of generality 00:41:35.960 --> 00:41:38.780 align:middle line:84% in the search for private information-constrained 00:41:38.780 --> 00:41:39.470 align:middle line:90% optimum. 00:41:39.470 --> 00:41:42.320 align:middle line:84% Now, there's an issue of language here. 00:41:42.320 --> 00:41:45.980 align:middle line:84% Instead of talking about a Pareto-optimal allocation, 00:41:45.980 --> 00:41:51.620 align:middle line:84% we should be talking about an information-constrained optimal 00:41:51.620 --> 00:41:52.790 align:middle line:90% allocation. 00:41:52.790 --> 00:41:56.750 align:middle line:84% Some people-- I don't love it-- talk about Pareto optimality 00:41:56.750 --> 00:42:00.800 align:middle line:84% as first best, and this notion of constrained optimality 00:42:00.800 --> 00:42:03.980 align:middle line:84% as second best, with the good intention of distinguishing 00:42:03.980 --> 00:42:05.180 align:middle line:90% those two cases. 00:42:05.180 --> 00:42:07.070 align:middle line:84% It's second best but unavoidable, 00:42:07.070 --> 00:42:10.190 align:middle line:84% because you cannot get around these kinds of incentive 00:42:10.190 --> 00:42:11.680 align:middle line:90% constraints. 00:42:11.680 --> 00:42:13.870 align:middle line:84% They may or may not be binding, but you definitely 00:42:13.870 --> 00:42:15.190 align:middle line:90% should be writing them down. 00:42:15.190 --> 00:42:17.710 align:middle line:84% And when they're binding, they constrain the solution, 00:42:17.710 --> 00:42:20.620 align:middle line:84% and hence the terminology "constrained optimum." 00:42:20.620 --> 00:42:21.595 align:middle line:90% Question so far? 00:42:21.595 --> 00:42:25.910 align:middle line:90% 00:42:25.910 --> 00:42:28.550 align:middle line:84% So what do we know about the solution? 00:42:28.550 --> 00:42:31.250 align:middle line:84% One thing I've already hinted at-- 00:42:31.250 --> 00:42:35.780 align:middle line:84% if there were full information, then if we go back, 00:42:35.780 --> 00:42:38.460 align:middle line:84% this is a version of what you've seen before. 00:42:38.460 --> 00:42:41.030 align:middle line:90% It's written out as two periods. 00:42:41.030 --> 00:42:44.510 align:middle line:84% But remember, the way we solve these things in Debreu decision 00:42:44.510 --> 00:42:48.020 align:middle line:84% tree, we said for any date and for any history of states 00:42:48.020 --> 00:42:51.560 align:middle line:84% leading up to that, we'll have a risk-sharing rule, a transfer 00:42:51.560 --> 00:42:54.980 align:middle line:84% rule, which is a function only of the current aggregate 00:42:54.980 --> 00:42:57.120 align:middle line:90% endowment and nothing else. 00:42:57.120 --> 00:43:00.020 align:middle line:84% So the full risk-sharing problem without the truth-telling 00:43:00.020 --> 00:43:04.260 align:middle line:84% constraints will devolve into a series of static problems, 00:43:04.260 --> 00:43:07.070 align:middle line:84% which means the transfer rule at day 1 00:43:07.070 --> 00:43:11.210 align:middle line:84% would be the same as the transfer rule at day 2. 00:43:11.210 --> 00:43:14.990 align:middle line:84% But in fact, when we have this information-constrained 00:43:14.990 --> 00:43:18.830 align:middle line:84% efficient arrangement, it's almost surely the case 00:43:18.830 --> 00:43:21.200 align:middle line:84% that we're not going to be able to get to the full risk 00:43:21.200 --> 00:43:22.310 align:middle line:90% sharing. 00:43:22.310 --> 00:43:28.250 align:middle line:84% And likewise, if you're already at the second date, 00:43:28.250 --> 00:43:29.900 align:middle line:84% you're kind of doomed, especially 00:43:29.900 --> 00:43:32.630 align:middle line:90% with one good, no lotteries. 00:43:32.630 --> 00:43:35.360 align:middle line:84% You can't have a theta 2-contingent transfer 00:43:35.360 --> 00:43:36.320 align:middle line:90% at the second date. 00:43:36.320 --> 00:43:38.810 align:middle line:84% But possibilities remain at the first date. 00:43:38.810 --> 00:43:40.100 align:middle line:90% Why? 00:43:40.100 --> 00:43:43.790 align:middle line:84% Precisely because you can tie the allocation rule 00:43:43.790 --> 00:43:45.770 align:middle line:84% in this lottery at the second date 00:43:45.770 --> 00:43:48.410 align:middle line:84% to what is announced at the first date. 00:43:48.410 --> 00:43:51.740 align:middle line:84% So this history of messages starts to matter. 00:43:51.740 --> 00:43:54.140 align:middle line:84% Or another way to put that, when it's 00:43:54.140 --> 00:43:57.980 align:middle line:84% necessary to have that, what happens at the second date 00:43:57.980 --> 00:44:00.350 align:middle line:90% is no longer a static problem. 00:44:00.350 --> 00:44:02.810 align:middle line:84% You have to utilize what also happened 00:44:02.810 --> 00:44:06.170 align:middle line:84% at the first date, which you could call a tie-in of sorts-- 00:44:06.170 --> 00:44:10.460 align:middle line:84% intertemporal cross-period ties in of the second date 00:44:10.460 --> 00:44:13.260 align:middle line:90% to the first date. 00:44:13.260 --> 00:44:18.110 align:middle line:84% It also reminded me of what the historians are talking about. 00:44:18.110 --> 00:44:21.530 align:middle line:84% They said, oh, these manners are terribly inefficient, 00:44:21.530 --> 00:44:23.720 align:middle line:90% bound by tradition. 00:44:23.720 --> 00:44:26.540 align:middle line:84% They can't break away from the past. 00:44:26.540 --> 00:44:30.260 align:middle line:84% Well, the theory we're going over 00:44:30.260 --> 00:44:32.930 align:middle line:84% says that there's a very good reason why they would 00:44:32.930 --> 00:44:34.970 align:middle line:90% like to be bound by the past-- 00:44:34.970 --> 00:44:38.110 align:middle line:90% for incentive purposes. 00:44:38.110 --> 00:44:40.890 align:middle line:84% So one example of that is borrowing and lending. 00:44:40.890 --> 00:44:43.470 align:middle line:84% I mean, suppose the villa has a low output, 00:44:43.470 --> 00:44:45.810 align:middle line:90% and they say, look, I promise-- 00:44:45.810 --> 00:44:48.330 align:middle line:84% let me pay less or borrow, and I'll 00:44:48.330 --> 00:44:50.730 align:middle line:90% repay the loan next period. 00:44:50.730 --> 00:44:52.680 align:middle line:84% And there's a commitment device to make sure 00:44:52.680 --> 00:44:54.630 align:middle line:90% that the loan will be repaid. 00:44:54.630 --> 00:44:59.790 align:middle line:84% So would the villa want to claim to be a lender when 00:44:59.790 --> 00:45:00.930 align:middle line:90% the income is low? 00:45:00.930 --> 00:45:03.480 align:middle line:84% No, they would want to be a borrower. 00:45:03.480 --> 00:45:05.257 align:middle line:84% And conversely, when the income is high, 00:45:05.257 --> 00:45:07.590 align:middle line:84% they're going to want to be a lender, as long as they're 00:45:07.590 --> 00:45:09.400 align:middle line:84% guaranteed of getting stuff back. 00:45:09.400 --> 00:45:12.060 align:middle line:90% So what's going on here? 00:45:12.060 --> 00:45:15.690 align:middle line:84% You're tying what happens at the second period 00:45:15.690 --> 00:45:17.880 align:middle line:84% to what happens at the first period-- 00:45:17.880 --> 00:45:21.000 align:middle line:84% those so-called intertemporal connections. 00:45:21.000 --> 00:45:23.460 align:middle line:84% It's not like you say a theta, and then you 00:45:23.460 --> 00:45:25.680 align:middle line:90% pay high or low today. 00:45:25.680 --> 00:45:28.530 align:middle line:84% You say a theta, you may pay high or low today, 00:45:28.530 --> 00:45:31.150 align:middle line:84% but there are consequences for tomorrow. 00:45:31.150 --> 00:45:35.460 align:middle line:84% So you choose what you're saying to give you 00:45:35.460 --> 00:45:37.350 align:middle line:90% the maximum possible utility. 00:45:37.350 --> 00:45:40.240 align:middle line:84% And you have an incentive to smooth consumption. 00:45:40.240 --> 00:45:41.880 align:middle line:84% So when you're low, you want to say so. 00:45:41.880 --> 00:45:42.380 align:middle line:90% Why? 00:45:42.380 --> 00:45:47.400 align:middle line:84% Because that's better for you in terms of getting money today, 00:45:47.400 --> 00:45:49.680 align:middle line:84% where you value it more than tomorrow, where 00:45:49.680 --> 00:45:52.740 align:middle line:90% you're likely to be higher. 00:45:52.740 --> 00:45:54.600 align:middle line:90% That was a bit of a digression. 00:45:54.600 --> 00:45:57.780 align:middle line:84% It also comes up at the bottom of the slide. 00:45:57.780 --> 00:46:00.210 align:middle line:84% So the borrowing and lending scheme 00:46:00.210 --> 00:46:04.500 align:middle line:84% is an example of the past mattering in a very trivial way 00:46:04.500 --> 00:46:05.940 align:middle line:90% with the borrowing and lending. 00:46:05.940 --> 00:46:07.830 align:middle line:84% What you've got to pay today is a function 00:46:07.830 --> 00:46:11.160 align:middle line:84% of whether you were a borrower or lender last time. 00:46:11.160 --> 00:46:13.350 align:middle line:90% It's not time consistent. 00:46:13.350 --> 00:46:16.470 align:middle line:84% By the time you roll around to day 2, 00:46:16.470 --> 00:46:22.290 align:middle line:84% and ask these guys whether they would like to start over, 00:46:22.290 --> 00:46:26.390 align:middle line:84% they're, like, yeah, sure, we can both be better off. 00:46:26.390 --> 00:46:29.030 align:middle line:84% The incentive constraint is imposed 00:46:29.030 --> 00:46:34.100 align:middle line:84% to get them to behave properly, as best they can, at date 1. 00:46:34.100 --> 00:46:37.910 align:middle line:84% Once date 1 has happened and we move to date 2, 00:46:37.910 --> 00:46:41.160 align:middle line:84% there is no longer a need for that constraint. 00:46:41.160 --> 00:46:45.800 align:middle line:84% And if we were to resolve the problem at day 2, 00:46:45.800 --> 00:46:48.330 align:middle line:84% they would likely do something different. 00:46:48.330 --> 00:46:51.760 align:middle line:84% So it's called "time inconsistent." 00:46:51.760 --> 00:46:54.760 align:middle line:84% The arrangement is not going to be consistently carried out 00:46:54.760 --> 00:46:57.790 align:middle line:90% over time, voluntarily. 00:46:57.790 --> 00:47:01.400 align:middle line:84% They're going to be bound by these rules. 00:47:01.400 --> 00:47:05.570 align:middle line:84% So then the thing at the bottom of the slide, claim 1-- 00:47:05.570 --> 00:47:08.500 align:middle line:84% borrowing and lending is not optimal. 00:47:08.500 --> 00:47:12.750 align:middle line:90% So let's go back to this. 00:47:12.750 --> 00:47:15.750 align:middle line:84% Say the solution to this program 8 00:47:15.750 --> 00:47:17.880 align:middle line:84% is the borrowing and lending solution. 00:47:17.880 --> 00:47:20.130 align:middle line:90% When theta is low, one borrows. 00:47:20.130 --> 00:47:24.952 align:middle line:84% When theta 1 is high, the agent lends, and re-pays back, 00:47:24.952 --> 00:47:26.910 align:middle line:84% with the payment going in the reverse direction 00:47:26.910 --> 00:47:28.710 align:middle line:90% in the second period. 00:47:28.710 --> 00:47:31.290 align:middle line:90% I claim that's not optimal. 00:47:31.290 --> 00:47:33.720 align:middle line:90% It's probably still mysterious. 00:47:33.720 --> 00:47:35.820 align:middle line:84% When the agent is low, he strictly 00:47:35.820 --> 00:47:40.230 align:middle line:84% prefers to say he's low rather than saying that he's high. 00:47:40.230 --> 00:47:43.980 align:middle line:84% That makes this inequality constraint strict. 00:47:43.980 --> 00:47:45.570 align:middle line:84% Likewise, when the agent is high, 00:47:45.570 --> 00:47:47.730 align:middle line:84% he strictly prefers to say he's high 00:47:47.730 --> 00:47:49.440 align:middle line:90% rather than saying he's low. 00:47:49.440 --> 00:47:51.900 align:middle line:84% That makes this inequality strict. 00:47:51.900 --> 00:47:55.080 align:middle line:84% Well, if both inequalities are strict, 00:47:55.080 --> 00:47:57.600 align:middle line:90% neither one can be binding. 00:47:57.600 --> 00:47:59.820 align:middle line:84% We might as well solve the programming problem 00:47:59.820 --> 00:48:02.010 align:middle line:84% as if they weren't there in the first place. 00:48:02.010 --> 00:48:04.120 align:middle line:84% Because now we know they're not binding. 00:48:04.120 --> 00:48:06.420 align:middle line:84% And what happens if you solve this problem 00:48:06.420 --> 00:48:08.340 align:middle line:90% without the constraints? 00:48:08.340 --> 00:48:10.410 align:middle line:84% That's the full risk-sharing problem. 00:48:10.410 --> 00:48:13.590 align:middle line:84% And it can't be optimal because they'll lie their head off 00:48:13.590 --> 00:48:16.690 align:middle line:84% about their income because there's no consequences. 00:48:16.690 --> 00:48:20.130 align:middle line:84% So that's the way to think through the bottom 00:48:20.130 --> 00:48:21.750 align:middle line:90% of this slide. 00:48:21.750 --> 00:48:25.200 align:middle line:84% Full insurance isn't feasible, not implementable 00:48:25.200 --> 00:48:27.900 align:middle line:84% because it's going to violate the incentive constraints. 00:48:27.900 --> 00:48:30.450 align:middle line:84% And borrowing and lending is not optimal, either. 00:48:30.450 --> 00:48:32.460 align:middle line:84% Which means, well, what is optimal? 00:48:32.460 --> 00:48:34.770 align:middle line:84% What is the actual solution to that program? 00:48:34.770 --> 00:48:39.180 align:middle line:84% Well, actually, it's a hybrid scheme 00:48:39.180 --> 00:48:42.210 align:middle line:84% that is a bit like risk-sharing, and borrowing, and lending. 00:48:42.210 --> 00:48:44.250 align:middle line:84% When you're low, you say you're low. 00:48:44.250 --> 00:48:46.733 align:middle line:84% You borrow, but you actually get even more money, 00:48:46.733 --> 00:48:48.150 align:middle line:84% but less money than you would have 00:48:48.150 --> 00:48:50.250 align:middle line:84% if it had been full risk sharing, 00:48:50.250 --> 00:48:53.030 align:middle line:84% and vice versa for when you're high. 00:48:53.030 --> 00:48:58.510 align:middle line:84% So it's a hybrid contract that is mixing up 00:48:58.510 --> 00:49:01.600 align:middle line:84% the two aspects, which makes sense 00:49:01.600 --> 00:49:03.500 align:middle line:84% because neither extreme is a good thing. 00:49:03.500 --> 00:49:05.970 align:middle line:90% So you end up in the middle. 00:49:05.970 --> 00:49:09.360 align:middle line:84% So this slide is about the other option 00:49:09.360 --> 00:49:10.890 align:middle line:90% I alluded to at the beginning. 00:49:10.890 --> 00:49:14.400 align:middle line:84% Let's revert back to a static problem. 00:49:14.400 --> 00:49:17.580 align:middle line:84% There's a cost K, use of resources, 00:49:17.580 --> 00:49:19.380 align:middle line:84% which the agent 2, the monastery, 00:49:19.380 --> 00:49:23.010 align:middle line:84% can incur in order to go and take a look at agent 1's 00:49:23.010 --> 00:49:23.970 align:middle line:90% actual outputs. 00:49:23.970 --> 00:49:27.360 align:middle line:84% So instead of claims about it, which will also happen, 00:49:27.360 --> 00:49:30.480 align:middle line:84% there's kind of like this possibility of an audit. 00:49:30.480 --> 00:49:34.620 align:middle line:84% It's as if in the US, you file your income tax returns 00:49:34.620 --> 00:49:37.650 align:middle line:84% making claims about stuff, but with a certain probability 00:49:37.650 --> 00:49:41.220 align:middle line:84% the IRS will audit you, and find out the truth of the matter. 00:49:41.220 --> 00:49:45.150 align:middle line:84% And if you're caught lying, you go to jail. 00:49:45.150 --> 00:49:48.180 align:middle line:84% That's how they got Al Capone, actually-- 00:49:48.180 --> 00:49:50.010 align:middle line:84% not for all the crimes, but because he 00:49:50.010 --> 00:49:51.550 align:middle line:90% misreported his income. 00:49:51.550 --> 00:49:53.340 align:middle line:90% So K is this audit cost. 00:49:53.340 --> 00:49:55.020 align:middle line:84% And we can introduce another variable 00:49:55.020 --> 00:49:59.250 align:middle line:90% called d, where d is the dummy. 00:49:59.250 --> 00:50:02.820 align:middle line:84% d equal 1 for audit or d equals 0 for not audit. 00:50:02.820 --> 00:50:06.780 align:middle line:84% And then we could enhance our transfers or the lotteries 00:50:06.780 --> 00:50:10.200 align:middle line:84% of transfers to depend on whether or not 00:50:10.200 --> 00:50:11.550 align:middle line:90% there's an audit-- 00:50:11.550 --> 00:50:14.370 align:middle line:84% equal 1 for an audit, equals 0 for not. 00:50:14.370 --> 00:50:16.290 align:middle line:84% When there's no audit, they have to rely 00:50:16.290 --> 00:50:19.200 align:middle line:84% on the filing of the return or the message that was sent. 00:50:19.200 --> 00:50:22.230 align:middle line:84% When there is an audit, they get to compare the message that 00:50:22.230 --> 00:50:25.150 align:middle line:90% was sent with the actual theta. 00:50:25.150 --> 00:50:27.225 align:middle line:84% And as you could imagine, going-- you 00:50:27.225 --> 00:50:30.950 align:middle line:84% could kill the guy, going to jail or whatever. 00:50:30.950 --> 00:50:35.920 align:middle line:84% So I'll spare you this slide except that the incentive 00:50:35.920 --> 00:50:38.500 align:middle line:84% constraint will now take advantage of the fact 00:50:38.500 --> 00:50:41.500 align:middle line:84% that lying is a pretty treacherous thing. 00:50:41.500 --> 00:50:43.870 align:middle line:84% Because with a certain positive probability, 00:50:43.870 --> 00:50:46.690 align:middle line:84% you'll get caught in the lie, and you can make 00:50:46.690 --> 00:50:48.730 align:middle line:90% the guy's utility really low. 00:50:48.730 --> 00:50:53.020 align:middle line:84% Later after class, you can look at this inequality constraint. 00:50:53.020 --> 00:50:57.520 align:middle line:84% It's this line here that you can make a very low number. 00:50:57.520 --> 00:51:00.430 align:middle line:84% Because you would penalize the guy if he said 00:51:00.430 --> 00:51:03.550 align:middle line:84% he was theta tilde, and he was actually revealed to be theta. 00:51:03.550 --> 00:51:05.050 align:middle line:84% And this is on the right-hand side 00:51:05.050 --> 00:51:06.790 align:middle line:90% of the incentive constraint. 00:51:06.790 --> 00:51:09.250 align:middle line:84% So the lower you can make this number, 00:51:09.250 --> 00:51:12.497 align:middle line:84% the easier it is to satisfy the incentive constraint, 00:51:12.497 --> 00:51:14.080 align:middle line:84% and the more you're going to move back 00:51:14.080 --> 00:51:16.960 align:middle line:84% toward the full information solution. 00:51:16.960 --> 00:51:20.860 align:middle line:84% But it comes at a cost, because this K 00:51:20.860 --> 00:51:25.180 align:middle line:84% is a cost, a real cost, that has to get subtracted off 00:51:25.180 --> 00:51:26.270 align:middle line:90% from resources. 00:51:26.270 --> 00:51:29.350 align:middle line:84% So when that cost K is very, very high, 00:51:29.350 --> 00:51:32.230 align:middle line:84% you will not be auditing very much. 00:51:32.230 --> 00:51:33.610 align:middle line:90% The audit will be random. 00:51:33.610 --> 00:51:35.470 align:middle line:84% And only rarely will you actually 00:51:35.470 --> 00:51:39.380 align:middle line:84% carry it out in order to conserve on resources. 00:51:39.380 --> 00:51:42.640 align:middle line:84% So at the beginning, I mentioned the institutional 00:51:42.640 --> 00:51:44.170 align:middle line:90% configuration. 00:51:44.170 --> 00:51:48.820 align:middle line:84% Is it true that those outlying villas doing their own farming 00:51:48.820 --> 00:51:53.140 align:middle line:84% were audited or audited less rarely than the ones close 00:51:53.140 --> 00:51:54.490 align:middle line:90% to the monastery? 00:51:54.490 --> 00:51:56.620 align:middle line:84% And this theory we just went through 00:51:56.620 --> 00:52:00.610 align:middle line:84% allows one to think about those as maybe what 00:52:00.610 --> 00:52:05.110 align:middle line:84% happened in practice, consistent with the institutional data. 00:52:05.110 --> 00:52:08.740 align:middle line:84% So I want to turn to the second part of the lecture, which 00:52:08.740 --> 00:52:12.970 align:middle line:84% has to do with mechanism design that we just did, but splice 00:52:12.970 --> 00:52:15.700 align:middle line:90% that into smart contracts. 00:52:15.700 --> 00:52:18.220 align:middle line:84% The shorthand for this is, think about a contract 00:52:18.220 --> 00:52:22.240 align:middle line:84% as a smart contract implemented with today's modern technology. 00:52:22.240 --> 00:52:24.730 align:middle line:84% We just talked about mechanism design 00:52:24.730 --> 00:52:28.030 align:middle line:84% as delivering contracts between a villa and a monastery 00:52:28.030 --> 00:52:30.300 align:middle line:90% as an example. 00:52:30.300 --> 00:52:32.910 align:middle line:84% And along the way, we'll talk about encryption, 00:52:32.910 --> 00:52:35.280 align:middle line:84% and hashes, and database management, 00:52:35.280 --> 00:52:37.260 align:middle line:90% and these protocols. 00:52:37.260 --> 00:52:40.500 align:middle line:84% Encryption-- we've talked about distributed ledgers. 00:52:40.500 --> 00:52:43.440 align:middle line:84% Encryption's like the third part of it. 00:52:43.440 --> 00:52:45.810 align:middle line:84% We talked about ledgers as transferring value, 00:52:45.810 --> 00:52:48.090 align:middle line:84% as in m-Pesa or other situations. 00:52:48.090 --> 00:52:52.320 align:middle line:84% We talked about ledgers as contracts to reconcile trades. 00:52:52.320 --> 00:52:54.570 align:middle line:84% This third thing is keeping secrets 00:52:54.570 --> 00:52:57.360 align:middle line:84% through encryption, which is logical to have here 00:52:57.360 --> 00:53:01.170 align:middle line:84% because we just got done talking about private information. 00:53:01.170 --> 00:53:02.040 align:middle line:90% Is it new? 00:53:02.040 --> 00:53:03.060 align:middle line:90% No, not at all. 00:53:03.060 --> 00:53:07.750 align:middle line:84% Encryption is ancient, literally thousands of years old. 00:53:07.750 --> 00:53:10.410 align:middle line:84% If you go back to Mesopotamia, they 00:53:10.410 --> 00:53:12.030 align:middle line:90% would be shipping goods around. 00:53:12.030 --> 00:53:14.640 align:middle line:84% They had created little tokens which they 00:53:14.640 --> 00:53:16.740 align:middle line:90% put in clay sealed envelopes. 00:53:16.740 --> 00:53:20.130 align:middle line:84% If the seal was broken, you'd know there was some tampering. 00:53:20.130 --> 00:53:22.020 align:middle line:84% And otherwise, when the goods arrived, 00:53:22.020 --> 00:53:24.450 align:middle line:84% the receiver of the goods can reconcile 00:53:24.450 --> 00:53:26.700 align:middle line:84% the goods in the shipment with this invoice, 00:53:26.700 --> 00:53:28.450 align:middle line:90% after breaking the seal. 00:53:28.450 --> 00:53:30.390 align:middle line:84% So those are clay in Mesopotamia, 00:53:30.390 --> 00:53:34.180 align:middle line:84% and that's where Mesopotamian writing came from, 00:53:34.180 --> 00:53:37.210 align:middle line:90% actually, is from these tokens. 00:53:37.210 --> 00:53:39.310 align:middle line:84% Or in medieval England, they had what 00:53:39.310 --> 00:53:42.250 align:middle line:84% they called "tally sticks," which were just wood, 00:53:42.250 --> 00:53:44.170 align:middle line:90% willow sticks. 00:53:44.170 --> 00:53:46.930 align:middle line:84% The borrower and the lender would make an agreement. 00:53:46.930 --> 00:53:50.770 align:middle line:84% The borrower would promise to repay. 00:53:50.770 --> 00:53:54.040 align:middle line:84% They would write these things on wooden ledgers 00:53:54.040 --> 00:53:55.880 align:middle line:90% and split it in half. 00:53:55.880 --> 00:53:59.980 align:middle line:84% And so the investor lender would have half of the stick 00:53:59.980 --> 00:54:01.690 align:middle line:84% and carry it around, could present it 00:54:01.690 --> 00:54:05.950 align:middle line:84% to the borrower for payment, but could also 00:54:05.950 --> 00:54:07.720 align:middle line:90% sell it to third parties. 00:54:07.720 --> 00:54:11.680 align:middle line:84% And so those willow sticks circulated around like money 00:54:11.680 --> 00:54:13.820 align:middle line:90% as a means of payment. 00:54:13.820 --> 00:54:16.340 align:middle line:84% The point of the willow-- it had unique grain, 00:54:16.340 --> 00:54:19.790 align:middle line:84% so you could match the stalk with the check. 00:54:19.790 --> 00:54:23.360 align:middle line:84% And if it didn't match, you know that the person presenting it 00:54:23.360 --> 00:54:25.140 align:middle line:90% is trying to commit some fraud. 00:54:25.140 --> 00:54:29.480 align:middle line:84% So it's another early example of encryption. 00:54:29.480 --> 00:54:33.600 align:middle line:84% Encryption today, intuitively-- this isn't quite right-- 00:54:33.600 --> 00:54:35.490 align:middle line:90% can be thought of factoring. 00:54:35.490 --> 00:54:39.440 align:middle line:84% So as you may know if you're MIT students trained in Computer 00:54:39.440 --> 00:54:42.110 align:middle line:84% Science, and Algebra, and so on, when 00:54:42.110 --> 00:54:44.310 align:middle line:84% you multiply two prime numbers together, 00:54:44.310 --> 00:54:46.550 align:middle line:90% you get another number-- 00:54:46.550 --> 00:54:50.390 align:middle line:84% 3 times 7, then 21, and you know how to factor it. 00:54:50.390 --> 00:54:53.810 align:middle line:84% But when those primes get big and are multiplied, 00:54:53.810 --> 00:54:57.380 align:middle line:84% it's virtually impossible to know 00:54:57.380 --> 00:55:01.580 align:middle line:84% what are the two numbers that were being multiplied together. 00:55:01.580 --> 00:55:05.150 align:middle line:84% So the output looks like an encrypted message. 00:55:05.150 --> 00:55:07.460 align:middle line:84% You can try to solve it, but you have 00:55:07.460 --> 00:55:09.620 align:middle line:84% to try all possible combinations. 00:55:09.620 --> 00:55:12.870 align:middle line:84% And it gets to be really hard to do that. 00:55:12.870 --> 00:55:15.780 align:middle line:84% Another way you can use factors, though, 00:55:15.780 --> 00:55:18.410 align:middle line:84% is to give someone part of the solution. 00:55:18.410 --> 00:55:22.460 align:middle line:84% Like here's the product encrypted, multiplied together, 00:55:22.460 --> 00:55:23.960 align:middle line:90% but I actually know the answer. 00:55:23.960 --> 00:55:25.340 align:middle line:84% I'll give you one of the factors. 00:55:25.340 --> 00:55:28.020 align:middle line:84% You can easily figure out the other factors. 00:55:28.020 --> 00:55:32.210 align:middle line:90% And so that's like hashes. 00:55:32.210 --> 00:55:36.170 align:middle line:84% The hash itself means nothing, but it is evidence of something 00:55:36.170 --> 00:55:39.410 align:middle line:84% if someone comes along and gives you one of both factors. 00:55:39.410 --> 00:55:41.210 align:middle line:84% Because then you can rehash the message 00:55:41.210 --> 00:55:44.480 align:middle line:84% and verify that the underlying message was the one that 00:55:44.480 --> 00:55:46.740 align:middle line:90% generated the hash. 00:55:46.740 --> 00:55:49.860 align:middle line:84% And finally, we come to cryptographic puzzles, 00:55:49.860 --> 00:55:53.950 align:middle line:84% which means the factors are big, but not too big. 00:55:53.950 --> 00:55:56.070 align:middle line:84% So then, you could imagine spinning 00:55:56.070 --> 00:55:58.050 align:middle line:84% the wheels of the combination of a safe 00:55:58.050 --> 00:56:01.380 align:middle line:84% to try to figure out which two factors generated the number. 00:56:01.380 --> 00:56:04.080 align:middle line:84% It's solvable, but it takes time. 00:56:04.080 --> 00:56:06.090 align:middle line:90% That's what Bitcoin uses-- 00:56:06.090 --> 00:56:09.010 align:middle line:84% these cryptographic puzzles, among other things. 00:56:09.010 --> 00:56:14.250 align:middle line:84% So the three objects, three types of things, 00:56:14.250 --> 00:56:17.550 align:middle line:84% are encryption, which is done now 00:56:17.550 --> 00:56:18.990 align:middle line:90% with private and public keys. 00:56:18.990 --> 00:56:21.540 align:middle line:84% And I'm happy to tell you more about that. 00:56:21.540 --> 00:56:25.380 align:middle line:84% I even have a primer that I wrote with Nicholas, a CS 00:56:25.380 --> 00:56:27.480 align:middle line:90% student here at MIT. 00:56:27.480 --> 00:56:29.280 align:middle line:84% Took me quite a while as an economist 00:56:29.280 --> 00:56:30.870 align:middle line:90% to understand this stuff. 00:56:30.870 --> 00:56:34.350 align:middle line:84% You probably heard, though, about public and private keys. 00:56:34.350 --> 00:56:36.780 align:middle line:84% The public key is used for encryption. 00:56:36.780 --> 00:56:40.200 align:middle line:84% The private key is used to decrypt the message. 00:56:40.200 --> 00:56:44.580 align:middle line:84% Hashing I've mentioned already, like multiplying factors 00:56:44.580 --> 00:56:45.870 align:middle line:90% together. 00:56:45.870 --> 00:56:49.620 align:middle line:84% Cryptographic puzzles, I guess I mentioned again-- 00:56:49.620 --> 00:56:51.690 align:middle line:84% the thing is to solve the puzzle, 00:56:51.690 --> 00:56:54.150 align:middle line:84% you don't spin the wheels of the safe. 00:56:54.150 --> 00:56:55.620 align:middle line:90% You actually run a computer. 00:56:55.620 --> 00:56:59.830 align:middle line:84% And that's where Bitcoin is chewing up all the electricity, 00:56:59.830 --> 00:57:02.770 align:middle line:84% as all these many miners are trying 00:57:02.770 --> 00:57:07.810 align:middle line:84% to find solutions to find the actual factors. 00:57:07.810 --> 00:57:11.080 align:middle line:90% So Bitcoin uses all three. 00:57:11.080 --> 00:57:14.090 align:middle line:84% It's actually pretty amazing and pretty complicated. 00:57:14.090 --> 00:57:17.140 align:middle line:84% It's using signature schemes, cryptographic puzzles, 00:57:17.140 --> 00:57:20.140 align:middle line:84% and something else I haven't talked about-- hashes 00:57:20.140 --> 00:57:21.340 align:middle line:90% with Merkle trees. 00:57:21.340 --> 00:57:26.200 align:middle line:84% But the entire history of the transactions on the ledger 00:57:26.200 --> 00:57:31.580 align:middle line:84% is hashed together with an identifier, 00:57:31.580 --> 00:57:34.700 align:middle line:84% allowing what's called Merkle trees as an economic way 00:57:34.700 --> 00:57:36.500 align:middle line:90% of storing all that data. 00:57:36.500 --> 00:57:38.090 align:middle line:90% Bitcoin uses proof of work. 00:57:38.090 --> 00:57:40.490 align:middle line:84% As I said, you need the equipment and the electricity 00:57:40.490 --> 00:57:43.070 align:middle line:84% to try to solve the cryptographic puzzle. 00:57:43.070 --> 00:57:45.560 align:middle line:84% The premise here is that it's kind of random 00:57:45.560 --> 00:57:46.850 align:middle line:90% who solves the puzzle. 00:57:46.850 --> 00:57:50.600 align:middle line:84% And the premise is most of the miners are honest. 00:57:50.600 --> 00:57:53.160 align:middle line:84% We'll come back to that momentarily. 00:57:53.160 --> 00:57:55.790 align:middle line:84% So since the larger number are honest, 00:57:55.790 --> 00:57:58.940 align:middle line:84% and the person that solves the puzzle is chosen at random, 00:57:58.940 --> 00:58:02.150 align:middle line:84% the guy solving the puzzle is likely to be honest. 00:58:02.150 --> 00:58:04.700 align:middle line:84% Hence, they validate the message. 00:58:04.700 --> 00:58:06.650 align:middle line:90% Another two objects here-- 00:58:06.650 --> 00:58:10.850 align:middle line:84% homomorphic encryption allows computation 00:58:10.850 --> 00:58:14.630 align:middle line:84% on top of cipher text for individual agents. 00:58:14.630 --> 00:58:18.200 align:middle line:84% And multiparty computation is a version 00:58:18.200 --> 00:58:21.200 align:middle line:84% of that that applies to multiple agents. 00:58:21.200 --> 00:58:25.290 align:middle line:84% It's easier to show you a little bit of the notation. 00:58:25.290 --> 00:58:26.870 align:middle line:90% So m is the message. 00:58:26.870 --> 00:58:31.770 align:middle line:84% Oh, yeah, M like message, like we just did. 00:58:31.770 --> 00:58:35.370 align:middle line:84% But the message is supposed to be private. 00:58:35.370 --> 00:58:37.980 align:middle line:84% On the right-hand side, you have this allocation rule 00:58:37.980 --> 00:58:40.560 align:middle line:84% or function, f, that seems to require 00:58:40.560 --> 00:58:43.980 align:middle line:84% the actual message, which means the message, if it's going 00:58:43.980 --> 00:58:46.560 align:middle line:84% to a third party, is revealed, whether it's 00:58:46.560 --> 00:58:49.180 align:middle line:90% Safaricom or something else. 00:58:49.180 --> 00:58:52.180 align:middle line:84% But on the left-hand side, there's 00:58:52.180 --> 00:58:56.430 align:middle line:84% another way to do this, which is as amazing as it is simple. 00:58:56.430 --> 00:58:58.720 align:middle line:84% You take the message m, and you encrypt it. 00:58:58.720 --> 00:59:01.270 align:middle line:84% Then you take the function f, which doesn't know what 00:59:01.270 --> 00:59:02.480 align:middle line:90% it's doing-- 00:59:02.480 --> 00:59:04.840 align:middle line:84% it's operating on the encrypted message. 00:59:04.840 --> 00:59:07.690 align:middle line:84% And if you decrypt the whole thing at the outcome, 00:59:07.690 --> 00:59:10.880 align:middle line:84% at the end of the day, you get the right answer. 00:59:10.880 --> 00:59:14.230 align:middle line:84% You get the stuff on the right-hand side. 00:59:14.230 --> 00:59:16.240 align:middle line:84% The encrypted space looks like junk. 00:59:16.240 --> 00:59:18.970 align:middle line:84% It's just all a bunch of bits, zeros, and ones, 00:59:18.970 --> 00:59:21.790 align:middle line:84% with hashes, and dollar signs, or whatever you want there. 00:59:21.790 --> 00:59:23.140 align:middle line:90% No one could possibly read it. 00:59:23.140 --> 00:59:26.060 align:middle line:84% That's what state of the art encryption is all about. 00:59:26.060 --> 00:59:28.270 align:middle line:84% So you take one thing and do something else. 00:59:28.270 --> 00:59:29.570 align:middle line:90% You can add them together. 00:59:29.570 --> 00:59:31.340 align:middle line:90% You can do rank ordering. 00:59:31.340 --> 00:59:33.010 align:middle line:90% It's like junk compared to junk. 00:59:33.010 --> 00:59:36.280 align:middle line:84% But it turns out that all those operations 00:59:36.280 --> 00:59:38.980 align:middle line:84% have meaning when done on the encrypted space. 00:59:38.980 --> 00:59:41.980 align:middle line:90% So homomorphic means isomorphic. 00:59:41.980 --> 00:59:45.640 align:middle line:84% Those underlying true message spaces and the encrypted spaces 00:59:45.640 --> 00:59:48.520 align:middle line:90% are equivalent to each other. 00:59:48.520 --> 00:59:51.610 align:middle line:84% It's on to one-to-one, and so on. 00:59:51.610 --> 00:59:54.500 align:middle line:84% Multi-party computation is very similar, 00:59:54.500 --> 00:59:56.230 align:middle line:84% except there are multiple agents. 00:59:56.230 --> 00:59:58.870 align:middle line:84% So this means that what you want to do 00:59:58.870 --> 01:00:01.000 align:middle line:84% is take inputs from the different agents, 01:00:01.000 --> 01:00:02.800 align:middle line:90% like their wealth. 01:00:02.800 --> 01:00:05.020 align:middle line:84% They want to see who is the richest guy. 01:00:05.020 --> 01:00:08.440 align:middle line:84% And they apply a function f, which is like a rank ordering, 01:00:08.440 --> 01:00:09.580 align:middle line:90% and get an outcome. 01:00:09.580 --> 01:00:11.950 align:middle line:84% But these guys don't want to reveal their wealth. 01:00:11.950 --> 01:00:14.860 align:middle line:84% They just want to know who is the richest guy. 01:00:14.860 --> 01:00:17.790 align:middle line:84% So another way to do this is take the afferent inputs 01:00:17.790 --> 01:00:19.170 align:middle line:90% from the agents, and encrypt it. 01:00:19.170 --> 01:00:21.120 align:middle line:84% Now nobody knows anything about what 01:00:21.120 --> 01:00:22.560 align:middle line:90% the other people are saying. 01:00:22.560 --> 01:00:27.090 align:middle line:84% You apply f to those encrypted messages-- 01:00:27.090 --> 01:00:29.100 align:middle line:90% fine-- in the encrypted space. 01:00:29.100 --> 01:00:30.210 align:middle line:90% No harm done. 01:00:30.210 --> 01:00:32.580 align:middle line:84% And then you decipher the whole thing, 01:00:32.580 --> 01:00:36.120 align:middle line:84% allowing, say, summaries like a rank ordering, 01:00:36.120 --> 01:00:39.360 align:middle line:84% without them ever knowing what the amount of wealth 01:00:39.360 --> 01:00:43.320 align:middle line:84% actually was, just who is the wealthiest guy. 01:00:43.320 --> 01:00:47.640 align:middle line:84% So that's called multiparty computation. 01:00:47.640 --> 01:00:49.740 align:middle line:84% Now, what's going on with these algorithms? 01:00:49.740 --> 01:00:52.620 align:middle line:84% We already talked about proof of work. 01:00:52.620 --> 01:00:54.300 align:middle line:90% Proof of work is Bitcoin. 01:00:54.300 --> 01:00:56.520 align:middle line:84% They're using electricity for the validation 01:00:56.520 --> 01:00:57.480 align:middle line:90% among the miners. 01:00:57.480 --> 01:01:02.490 align:middle line:84% Proof of stake is another one, where the validation happens, 01:01:02.490 --> 01:01:05.980 align:middle line:84% but instead of chewing up electricity, they get to vote. 01:01:05.980 --> 01:01:09.690 align:middle line:84% And their vote counts more if they hold more coins. 01:01:09.690 --> 01:01:13.710 align:middle line:84% Byzantine fault tolerance-- another algorithm-- 01:01:13.710 --> 01:01:16.140 align:middle line:84% this, one especially the practical one, 01:01:16.140 --> 01:01:18.270 align:middle line:84% is what I was alluding to before. 01:01:18.270 --> 01:01:21.330 align:middle line:84% If there are f failing nodes that are either 01:01:21.330 --> 01:01:25.530 align:middle line:84% faulty computers, or malicious actors like hackers, 01:01:25.530 --> 01:01:31.290 align:middle line:84% you just need 3 times f plus 1 replicas in order 01:01:31.290 --> 01:01:34.560 align:middle line:84% to be sure that you've got a safe algorithm. 01:01:34.560 --> 01:01:38.280 align:middle line:84% Because you can compare across enough 01:01:38.280 --> 01:01:42.270 align:middle line:84% of the entities who are safe to be able to figure out who 01:01:42.270 --> 01:01:43.470 align:middle line:90% was faulty. 01:01:43.470 --> 01:01:46.140 align:middle line:84% Federated Byzantine agents decide 01:01:46.140 --> 01:01:50.460 align:middle line:84% not to rely on a third party to do the validation. 01:01:50.460 --> 01:01:51.670 align:middle line:90% They don't trust each other. 01:01:51.670 --> 01:01:54.300 align:middle line:84% But they can name the people they trust the most, 01:01:54.300 --> 01:01:57.180 align:middle line:84% and you have overlapping circles of trust. 01:01:57.180 --> 01:02:03.510 align:middle line:84% And Stellar is a version of that FBA protocol. 01:02:03.510 --> 01:02:06.300 align:middle line:90% Now, what else about protocols? 01:02:06.300 --> 01:02:09.720 align:middle line:84% Nakamoto was very clever in giving Bitcoin miners 01:02:09.720 --> 01:02:13.650 align:middle line:84% an incentive to mine properly and not conceal outcomes, 01:02:13.650 --> 01:02:16.000 align:middle line:84% to be running the machines, and so on. 01:02:16.000 --> 01:02:18.810 align:middle line:84% But it turns out it is subject to some problems 01:02:18.810 --> 01:02:19.770 align:middle line:90% like collusion. 01:02:19.770 --> 01:02:23.130 align:middle line:84% So the economists have jumped in and have become very critical, 01:02:23.130 --> 01:02:25.960 align:middle line:84% although evidently, collusion has never actually happened, 01:02:25.960 --> 01:02:28.930 align:middle line:84% even though the number of miners is very small. 01:02:28.930 --> 01:02:32.370 align:middle line:84% Steve Morris, my colleague, and Hyun Song Shin, now at the BIS, 01:02:32.370 --> 01:02:35.100 align:middle line:84% looked at a classic problem in computer science called 01:02:35.100 --> 01:02:36.960 align:middle line:90% the Byzantine Generals problem. 01:02:36.960 --> 01:02:41.280 align:middle line:84% And it has the property that it's not incentive compatible. 01:02:41.280 --> 01:02:44.130 align:middle line:84% Even though generals have an incentive 01:02:44.130 --> 01:02:47.400 align:middle line:84% to truthfully announce messages and send them to each other, 01:02:47.400 --> 01:02:50.190 align:middle line:84% it turns out if you put it in the context of what we just 01:02:50.190 --> 01:02:51.120 align:middle line:90% did-- 01:02:51.120 --> 01:02:54.210 align:middle line:84% a multi-agent mechanism design problem-- 01:02:54.210 --> 01:02:57.270 align:middle line:84% they will not follow the prescribed protocol. 01:02:57.270 --> 01:02:59.490 align:middle line:84% It's not in their self interest, when 01:02:59.490 --> 01:03:01.710 align:middle line:84% they start doing Bayesian analysis, 01:03:01.710 --> 01:03:04.200 align:middle line:84% trying to figure out what the other general knows. 01:03:04.200 --> 01:03:06.960 align:middle line:84% So you can just impose the algorithm and hope 01:03:06.960 --> 01:03:08.160 align:middle line:90% people follow it. 01:03:08.160 --> 01:03:11.230 align:middle line:84% But from what we did today, that's a bit treacherous. 01:03:11.230 --> 01:03:14.160 align:middle line:84% You really want to look at the incentive of the validators 01:03:14.160 --> 01:03:15.690 align:middle line:90% to follow the protocol. 01:03:15.690 --> 01:03:18.750 align:middle line:84% And that's where we come to mechanism design. 01:03:18.750 --> 01:03:20.280 align:middle line:84% In fact, with mechanism design, we 01:03:20.280 --> 01:03:23.400 align:middle line:84% don't even need to worry about agents telling the truth. 01:03:23.400 --> 01:03:27.180 align:middle line:84% We don't need to monitor or validate their messages. 01:03:27.180 --> 01:03:29.130 align:middle line:84% The revelation principle tells us 01:03:29.130 --> 01:03:31.830 align:middle line:84% that agents will tell the truth if we set up 01:03:31.830 --> 01:03:33.660 align:middle line:90% the contract properly. 01:03:33.660 --> 01:03:37.410 align:middle line:84% And not only that, we can record past messages the way 01:03:37.410 --> 01:03:39.660 align:middle line:84% we did in that multi-agent problem. 01:03:39.660 --> 01:03:42.210 align:middle line:84% Past messages just get put on the ledger. 01:03:42.210 --> 01:03:44.640 align:middle line:84% Because of the signature schemes, 01:03:44.640 --> 01:03:47.800 align:middle line:84% we can be sure that they are valid, 01:03:47.800 --> 01:03:52.320 align:middle line:84% they haven't been tampered with over time, and so on. 01:03:52.320 --> 01:03:56.360 align:middle line:84% So where we're going is to implement the mechanism design 01:03:56.360 --> 01:03:59.870 align:middle line:84% problem as a smart contract with the code, 01:03:59.870 --> 01:04:02.180 align:middle line:84% meaning like dynamic programming, 01:04:02.180 --> 01:04:06.200 align:middle line:84% you just map states into outcomes with contingencies. 01:04:06.200 --> 01:04:09.110 align:middle line:84% So you've already seen this in the dynamic programs 01:04:09.110 --> 01:04:11.000 align:middle line:90% that we've solved. 01:04:11.000 --> 01:04:14.720 align:middle line:84% And you can separate out that contracting part 01:04:14.720 --> 01:04:16.220 align:middle line:90% from the ledgers. 01:04:16.220 --> 01:04:19.260 align:middle line:84% We just have people agree to the code, experiment with it, 01:04:19.260 --> 01:04:23.000 align:middle line:84% make sure it works, set up your encryption scheme. 01:04:23.000 --> 01:04:26.360 align:middle line:84% And then it's like having an auction without an auctioneer. 01:04:26.360 --> 01:04:28.940 align:middle line:84% We're implementing that hybrid borrowing/lending scheme 01:04:28.940 --> 01:04:31.100 align:middle line:90% without having a third party. 01:04:31.100 --> 01:04:33.720 align:middle line:84% It's just done by the parties themselves. 01:04:33.720 --> 01:04:37.160 align:middle line:84% And encryption, MPC and homomorphic encryption, 01:04:37.160 --> 01:04:40.130 align:middle line:84% make sure that all the messages are private, 01:04:40.130 --> 01:04:43.670 align:middle line:84% and nobody gets to see those values. 01:04:43.670 --> 01:04:45.200 align:middle line:84% And then at the end of the day, you 01:04:45.200 --> 01:04:47.630 align:middle line:84% can kick in the borrowing and lending scheme 01:04:47.630 --> 01:04:51.020 align:middle line:84% so that for example, if it's a loan, 01:04:51.020 --> 01:04:53.300 align:middle line:84% it's going to be repaid because the loan is 01:04:53.300 --> 01:04:54.380 align:middle line:90% backed by collateral. 01:04:54.380 --> 01:04:58.040 align:middle line:84% So that would involve a transfer on the ledgers. 01:04:58.040 --> 01:05:00.033 align:middle line:84% So I'm not against the distributed ledgers. 01:05:00.033 --> 01:05:01.950 align:middle line:84% As I said, I just wrote a whole book about it. 01:05:01.950 --> 01:05:03.620 align:middle line:84% But I just want to point out what 01:05:03.620 --> 01:05:06.470 align:middle line:84% we did today, with the privacy and the messages 01:05:06.470 --> 01:05:09.350 align:middle line:84% and all of that, can be done with encryption, 01:05:09.350 --> 01:05:14.930 align:middle line:84% and allows smart contracts to be executed on the ledgers. 01:05:14.930 --> 01:05:15.950 align:middle line:90% All right. 01:05:15.950 --> 01:05:17.630 align:middle line:84% Well, I went over by a minute, and I 01:05:17.630 --> 01:05:20.130 align:middle line:90% was rushing a bit at the end. 01:05:20.130 --> 01:05:23.510 align:middle line:84% So take a look at these slides, especially toward the end. 01:05:23.510 --> 01:05:27.080 align:middle line:84% And see if you can map this encryption back 01:05:27.080 --> 01:05:29.810 align:middle line:84% into the earlier part of the lecture. 01:05:29.810 --> 01:05:31.890 align:middle line:90% That's really the main point. 01:05:31.890 --> 01:05:34.270 align:middle line:90% And I will let you go. 01:05:34.270 --> 01:05:40.000 align:middle line:90%