WEBVTT 00:00:00.040 --> 00:00:02.460 The following content is provided under a Creative 00:00:02.460 --> 00:00:03.870 Commons license. 00:00:03.870 --> 00:00:06.910 Your support will help MIT OpenCourseWare continue to 00:00:06.910 --> 00:00:10.560 offer high-quality educational resources for free. 00:00:10.560 --> 00:00:13.460 To make a donation or view additional materials from 00:00:13.460 --> 00:00:16.180 hundreds of MIT courses, visit mitopencourseware@ocw.mit.edu. 00:00:24.830 --> 00:00:25.920 PROFESSOR: Economics-- 00:00:25.920 --> 00:00:27.510 oligopoly. 00:00:27.510 --> 00:00:34.390 Which is basically trying to move towards the most 00:00:34.390 --> 00:00:39.150 realistic modeling of markets that we can. 00:00:39.150 --> 00:00:42.820 We've talked about two extreme versions of modeling markets. 00:00:42.820 --> 00:00:47.610 One is perfect competition, which is the extreme case of 00:00:47.610 --> 00:00:49.490 perfect entry and exit. 00:00:49.490 --> 00:00:50.920 Free entry and exit. 00:00:50.920 --> 00:00:52.630 Perfect consumer information. 00:00:52.630 --> 00:00:53.950 An idealized market. 00:00:53.950 --> 00:00:56.810 We know that doesn't really exist in practice anywhere. 00:00:56.810 --> 00:00:59.510 The second extreme was monopoly, which we do see in 00:00:59.510 --> 00:01:00.880 practice in some places. 00:01:00.880 --> 00:01:04.140 In particular, when there's natural monopolies. 00:01:04.140 --> 00:01:04.940 We do see that. 00:01:04.940 --> 00:01:07.520 But that's still doesn't describe most markets. 00:01:07.520 --> 00:01:10.970 Most markets are better described as oligopolies. 00:01:10.970 --> 00:01:14.160 These are markets where there's more than one market 00:01:14.160 --> 00:01:18.000 player, yet where each firm is large enough to actually 00:01:18.000 --> 00:01:20.430 affect the price. 00:01:20.430 --> 00:01:23.880 So an oligopoly market is where there'll be a small 00:01:23.880 --> 00:01:27.660 number of firms in the market with substantial barriers to 00:01:27.660 --> 00:01:31.190 entry from additional firms. An oligopoly market where 00:01:31.190 --> 00:01:34.300 there's a small number of firms with enough barriers to 00:01:34.300 --> 00:01:37.960 entry that additional firms don't enter. 00:01:37.960 --> 00:01:40.680 So the classic example of an oligopoly 00:01:40.680 --> 00:01:43.250 industry is the auto industry. 00:01:43.250 --> 00:01:47.000 Here's a market with a small number of dominant players. 00:01:47.000 --> 00:01:50.200 There's been some entry and exit over time, obviously, but 00:01:50.200 --> 00:01:51.870 it moves pretty slowly. 00:01:51.870 --> 00:01:53.850 By and large it's a market where there's 00:01:53.850 --> 00:01:55.780 very limited entry. 00:01:55.780 --> 00:02:00.110 And the question is, how do firms behave in this market? 00:02:00.110 --> 00:02:02.700 Obviously it's not like perfect competition where they 00:02:02.700 --> 00:02:05.750 can lazily take a price out of the market and just produce 00:02:05.750 --> 00:02:07.290 based on that price. 00:02:07.290 --> 00:02:09.199 But it's also not the same as monopoly where they can just 00:02:09.199 --> 00:02:10.639 get to set the price and not worry about what 00:02:10.639 --> 00:02:11.890 other people do. 00:02:11.890 --> 00:02:14.470 They're in this in-between situation where they have 00:02:14.470 --> 00:02:15.630 price setting power. 00:02:15.630 --> 00:02:18.220 They have some market power but in a context where they 00:02:18.220 --> 00:02:21.830 have to worry about competitors. 00:02:21.830 --> 00:02:25.510 And so in this context there are two different ways firms 00:02:25.510 --> 00:02:28.450 can behave. It's important to lay out to start. 00:02:28.450 --> 00:02:29.990 There's two different ways for firms to behave. They can 00:02:29.990 --> 00:02:34.130 behave cooperatively or non-cooperatively. 00:02:34.130 --> 00:02:36.510 If they behave cooperatively we say 00:02:36.510 --> 00:02:38.046 that they form a cartel. 00:02:40.620 --> 00:02:46.110 So our cartel is what happens when oligopolistic firms, when 00:02:46.110 --> 00:02:50.450 firms in an oligopolistic market behave cooperatively to 00:02:50.450 --> 00:02:51.220 determine the outcome. 00:02:51.220 --> 00:02:53.480 We call that a cartel. 00:02:53.480 --> 00:02:56.410 The classic example, of course, here being OPEC. 00:02:56.410 --> 00:02:59.680 The Organization of Petroleum Exporting Countries, which is 00:02:59.680 --> 00:03:04.830 a cartel that drives the price of oil. 00:03:04.830 --> 00:03:07.950 Those countries cooperate in how much oil they produce to 00:03:07.950 --> 00:03:09.880 move the price up or down according to 00:03:09.880 --> 00:03:12.930 what the group desires. 00:03:12.930 --> 00:03:18.170 And what cartels do is essentially turn oligopolies 00:03:18.170 --> 00:03:20.010 into monopolies. 00:03:20.010 --> 00:03:22.610 So what cartelization does, what a cooperative equilibrium 00:03:22.610 --> 00:03:25.380 does is essentially say, let's all get together and behave as 00:03:25.380 --> 00:03:26.905 if we're one big monopoly by cooperating. 00:03:30.130 --> 00:03:32.320 And therefore, if you cooperate you can get all the 00:03:32.320 --> 00:03:34.580 wonderful things monopolies get: huge market power, huge 00:03:34.580 --> 00:03:36.090 markets et cetera. 00:03:36.090 --> 00:03:38.760 But as we'll talk about next time, it turns out to be 00:03:38.760 --> 00:03:43.080 pretty hard to get a cooperative oligopoly. 00:03:43.080 --> 00:03:45.870 There's lots of reasons why it might fall apart. 00:03:45.870 --> 00:03:49.820 And that's why in most oligopolistic markets firms 00:03:49.820 --> 00:03:52.110 behave non cooperatively. 00:03:52.110 --> 00:03:55.160 In most oligopolistic markets firms are behaving 00:03:55.160 --> 00:03:56.490 non-cooperatively. 00:03:56.490 --> 00:04:00.360 They're competing with each other, not cooperating. 00:04:00.360 --> 00:04:03.900 And that's what we're going to spend today analyzing is the 00:04:03.900 --> 00:04:05.920 case of non-cooperative oligopolies. 00:04:17.420 --> 00:04:17.820 Yeah? 00:04:17.820 --> 00:04:19.070 AUDIENCE: [INAUDIBLE]? 00:04:21.660 --> 00:04:23.060 PROFESSOR: Depends on the context. 00:04:25.970 --> 00:04:28.470 In the US, and I'll talk about this, in the US there's 00:04:28.470 --> 00:04:31.860 anti-trust legislation which can make it illegal in many 00:04:31.860 --> 00:04:33.730 contexts to cooperate. 00:04:33.730 --> 00:04:37.600 Obviously OPEC is not subject to some world legislation. 00:04:37.600 --> 00:04:39.490 But even in the US there can be implicit cartelization and 00:04:39.490 --> 00:04:43.600 implicit cooperation, and we'll talk about that. 00:04:43.600 --> 00:04:45.020 It's a good question. 00:04:45.020 --> 00:04:46.050 So technically you're right. 00:04:46.050 --> 00:04:49.890 Technically it is illegal in the US in most contexts to 00:04:49.890 --> 00:04:52.470 form a cooperative, to form a cartel. 00:04:52.470 --> 00:04:55.780 Whether in practice those laws can be enforced is an 00:04:55.780 --> 00:04:57.040 interesting, legitimate question. 00:04:59.640 --> 00:05:02.050 So today we want to focus on the case of non-cooperative 00:05:02.050 --> 00:05:02.500 oligopolies. 00:05:02.500 --> 00:05:06.030 And to do so we're going to turn to a new tool. 00:05:06.030 --> 00:05:08.440 And one of the fundamental tools of economics in the last 00:05:08.440 --> 00:05:11.370 30 years which is game theory. 00:05:11.370 --> 00:05:15.050 So today we're going to talk about game theory. 00:05:15.050 --> 00:05:20.310 Game theory is a tool of economics that was not really 00:05:20.310 --> 00:05:25.640 used early in economics but has come to dominate 00:05:25.640 --> 00:05:30.210 theoretical economics over the past 30 or 40 years. 00:05:30.210 --> 00:05:33.820 And basically the way that game theory works is to think, 00:05:33.820 --> 00:05:38.790 literally, of oligopolistic firms as engaging in a game. 00:05:38.790 --> 00:05:42.420 So when you play, don't want to say play Monopoly, that's 00:05:42.420 --> 00:05:43.980 confusing terms. When you play Sorry! 00:05:43.980 --> 00:05:48.200 or whatever with someone, or play some online game with 00:05:48.200 --> 00:05:50.200 someone, you're competing to win. 00:05:50.200 --> 00:05:52.240 You're behaving non-cooperatively. 00:05:52.240 --> 00:05:54.250 You're competing to win. 00:05:54.250 --> 00:05:58.100 So basically what the insights of game theory are that all 00:05:58.100 --> 00:06:00.770 the tools we used strategically to make 00:06:00.770 --> 00:06:04.940 decisions in playing games can actually be used in modeling 00:06:04.940 --> 00:06:07.170 how firms compete non-cooperatively in 00:06:07.170 --> 00:06:08.420 oligopolistic market. 00:06:11.330 --> 00:06:17.010 The key insight is that each firm will develop a strategy. 00:06:17.010 --> 00:06:20.370 Just as when you're playing chess you have some strategy 00:06:20.370 --> 00:06:24.420 going in, firms develop a strategy. 00:06:24.420 --> 00:06:27.580 And that based on that strategy they will determine 00:06:27.580 --> 00:06:30.380 their behavior. 00:06:30.380 --> 00:06:36.470 And what is going to determine that behavior is going to be 00:06:36.470 --> 00:06:42.010 how firms' strategies combine to determine a market outcome. 00:06:42.010 --> 00:06:44.910 When firms come in with different strategies, or when 00:06:44.910 --> 00:06:46.560 a bunch of firms with strategies come in to compete 00:06:46.560 --> 00:06:50.355 with each other, what determines the market outcome. 00:06:50.355 --> 00:06:53.790 And what that's going to depend on is something we call 00:06:53.790 --> 00:06:55.305 an equilibrium concept. 00:06:59.940 --> 00:07:02.080 Which is how do we measure-- 00:07:02.080 --> 00:07:05.610 essentially the equilibrium concept is in game theory 00:07:05.610 --> 00:07:06.750 terms, think about how do we determine 00:07:06.750 --> 00:07:08.490 when the game's over? 00:07:08.490 --> 00:07:11.510 How do we determine when we've decided on the 00:07:11.510 --> 00:07:13.160 outcome of the market. 00:07:13.160 --> 00:07:14.260 What's the equilibrium concept? 00:07:14.260 --> 00:07:18.170 So when you're reading the rules of a new game the first 00:07:18.170 --> 00:07:20.230 thing you look for is how do you decide who wins. 00:07:20.230 --> 00:07:22.530 That's kind of like what the equilibrium concept is. 00:07:22.530 --> 00:07:26.900 It's what determines whether the game has ended. 00:07:26.900 --> 00:07:30.760 What determines whether you've reached equilibrium. 00:07:30.760 --> 00:07:33.170 Where you've reached a point where the market is stable and 00:07:33.170 --> 00:07:34.650 therefore the game has ended. 00:07:34.650 --> 00:07:36.390 Not ended in the sense the firm shut down, but ended in 00:07:36.390 --> 00:07:38.390 the sense that you know what everybody's doing. 00:07:38.390 --> 00:07:40.060 So it's not quite like winning or losing. 00:07:40.060 --> 00:07:41.870 It's more just like what determines when you're at the 00:07:41.870 --> 00:07:46.490 point where that market is at equilibrium. 00:07:46.490 --> 00:07:51.150 Now the most famous concept is due to John Nash, who many of 00:07:51.150 --> 00:07:53.900 you heard of from the movie and book A Beautiful Mind, and 00:07:53.900 --> 00:07:55.390 that's called the Nash Equilibrium. 00:08:01.210 --> 00:08:07.850 A Nash equilibrium is the point at which no firm wants 00:08:07.850 --> 00:08:11.030 to change its strategy given what the 00:08:11.030 --> 00:08:12.900 other firms are doing. 00:08:12.900 --> 00:08:13.860 I'm going to say that again. 00:08:13.860 --> 00:08:17.030 A Nash equilibrium is the point where no firm wants to 00:08:17.030 --> 00:08:21.940 change its strategy given what the other firms are doing. 00:08:21.940 --> 00:08:25.210 It's a little bit bizarre, but we'll work it out. 00:08:25.210 --> 00:08:31.230 In other words, more formally, the idea is that holding 00:08:31.230 --> 00:08:38.169 constant, given the strategies all your competitors use 00:08:38.169 --> 00:08:43.390 there's nothing that I can do to raise my profits further. 00:08:43.390 --> 00:08:46.640 Given the strategies all my competitors are playing, 00:08:46.640 --> 00:08:50.080 there's no strategy I can choose that will make me more 00:08:50.080 --> 00:08:52.110 profitable than the one I'm choosing. 00:08:52.110 --> 00:08:54.257 And likewise for every player in the market that will turn 00:08:54.257 --> 00:08:54.930 out to be true. 00:08:54.930 --> 00:08:56.860 So have players sitting around a game board, 00:08:56.860 --> 00:08:58.340 going around the circle. 00:08:58.340 --> 00:09:01.110 Each player says, given what I know each of the rest you are 00:09:01.110 --> 00:09:04.560 doing, I'm doing the best thing I can. 00:09:04.560 --> 00:09:06.780 And they go around the circle and everybody says, OK, I'm at 00:09:06.780 --> 00:09:08.050 that point. 00:09:08.050 --> 00:09:11.580 You've reached a stable Nash equilibrium. 00:09:11.580 --> 00:09:14.100 This was named, of course, for John Nash. 00:09:14.100 --> 00:09:15.530 You all know the story of John Nash. 00:09:15.530 --> 00:09:17.820 He was a famous, actually mathematician. 00:09:17.820 --> 00:09:21.650 We use his tools in economics, but he was a mathematician. 00:09:21.650 --> 00:09:23.770 Developed these incredible theories, and then developed 00:09:23.770 --> 00:09:25.920 schizophrenia, went crazy. 00:09:25.920 --> 00:09:29.010 But not before he developed some of the most important 00:09:29.010 --> 00:09:31.770 concepts in both mathematics and economics. 00:09:31.770 --> 00:09:34.460 The most important is the Nash equilibrium. 00:09:34.460 --> 00:09:39.170 Now the best illustration we use of the Nash equilibrium is 00:09:39.170 --> 00:09:41.680 an example that we refer to as the prisoner's dilemma. 00:09:48.380 --> 00:09:51.920 And many of you will be familiar with this from more 00:09:51.920 --> 00:09:53.330 popular reading you've done in economics. 00:09:53.330 --> 00:09:55.200 But let me just go through it because it's important to 00:09:55.200 --> 00:09:55.760 understand it. 00:09:55.760 --> 00:09:57.000 The prisoner's dilemma. 00:09:57.000 --> 00:10:01.960 The prisoner's dilemma the title comes from the old way 00:10:01.960 --> 00:10:03.370 they used to make police movies. 00:10:03.370 --> 00:10:06.670 Where the idea is you catch two guys at a crime. 00:10:06.670 --> 00:10:10.010 You can't put them away unless one of them fesses up. 00:10:10.010 --> 00:10:12.680 So what you do is you put them each a separate room. 00:10:12.680 --> 00:10:16.090 And you say to the one, your buddy's cracked. 00:10:16.090 --> 00:10:18.890 He's going to he's going to sell you down the river. 00:10:18.890 --> 00:10:22.610 You better, I'm using all my '50s analogies, he's going to 00:10:22.610 --> 00:10:25.010 put you away for good. 00:10:25.010 --> 00:10:28.530 But if you admit that he's guilty and he did the crime, 00:10:28.530 --> 00:10:30.980 we'll let you off with a light sentence. 00:10:30.980 --> 00:10:32.660 Then they go to the other room and say the same thing to the 00:10:32.660 --> 00:10:35.490 other guy hoping they'll both rat on each other and they'll 00:10:35.490 --> 00:10:38.580 both get a sentence. 00:10:38.580 --> 00:10:46.360 So basically the idea is, let's say that you walk into 00:10:46.360 --> 00:10:49.030 each room and you say to each person, look, we have enough 00:10:49.030 --> 00:10:51.330 evidence right here, and you show them, to send you each to 00:10:51.330 --> 00:10:53.850 prison for a year. 00:10:53.850 --> 00:10:55.400 We would have enough evidence to send you each to 00:10:55.400 --> 00:10:56.970 prison for a year. 00:10:56.970 --> 00:11:01.450 But we aren't sure about this other thing. 00:11:01.450 --> 00:11:03.980 If you'll admit that your friend did this other thing, 00:11:03.980 --> 00:11:06.834 then he'll go for five years and you'll go free. 00:11:06.834 --> 00:11:08.700 And then we go to the friend and say the same thing. 00:11:08.700 --> 00:11:10.360 If you'll admit that your friend did the other thing 00:11:10.360 --> 00:11:11.770 he'll go five years and you'll go free. 00:11:11.770 --> 00:11:17.070 But if they both admit then they both go for two years. 00:11:17.070 --> 00:11:18.980 So if they both admit, they both go for two years. 00:11:18.980 --> 00:11:21.360 Now the way to write this down, what we do here to 00:11:21.360 --> 00:11:25.410 explain this, is we write down what we call a payoff matrix. 00:11:25.410 --> 00:11:27.000 So write down a payoff matrix. 00:11:27.000 --> 00:11:31.640 So the idea is we have prisoner A here 00:11:31.640 --> 00:11:32.980 and prisoner B here. 00:11:36.910 --> 00:11:38.510 And they each have an option. 00:11:38.510 --> 00:11:43.300 They could remain silent or they can talk. 00:11:47.990 --> 00:11:49.240 Silent or talk. 00:11:52.270 --> 00:11:55.370 Now if they both remain silent, if they both say I 00:11:55.370 --> 00:11:57.780 would never rat out my friend, I'm happy to go to jail for a 00:11:57.780 --> 00:12:00.910 year rather than rat out my friend, then they each get one 00:12:00.910 --> 00:12:01.950 year in jail. 00:12:01.950 --> 00:12:04.890 a equals 1, b equals 1. 00:12:04.890 --> 00:12:11.020 However if prisoner A rats out his buddy and prisoner B 00:12:11.020 --> 00:12:15.785 chooses not to rat out his buddy, then A gets-- 00:12:18.345 --> 00:12:21.360 so I'm sorry, if prisoner A talks and 00:12:21.360 --> 00:12:23.210 prisoner B remains silent. 00:12:23.210 --> 00:12:26.230 Prisoner A talks, prisoner B remains silent, then A gets 00:12:26.230 --> 00:12:29.050 zero but B get five years in prison. 00:12:31.650 --> 00:12:35.520 On the other hand, if prisoner B rats out his friend, but a 00:12:35.520 --> 00:12:39.190 prisoner A is true and doesn't say anything, then prisoner A 00:12:39.190 --> 00:12:42.080 is going to get stuck with five years and prisoner B is 00:12:42.080 --> 00:12:44.140 going to get nothing. 00:12:44.140 --> 00:12:47.300 And if they both rat each other out then they 00:12:47.300 --> 00:12:48.550 both get two years. 00:12:55.430 --> 00:12:57.080 So people understand the payoff. 00:12:57.080 --> 00:12:59.150 Are there questions about the set-up here? 00:12:59.150 --> 00:13:01.150 This is complicated so got to make sure you 00:13:01.150 --> 00:13:03.220 understand the set-up. 00:13:03.220 --> 00:13:08.390 Now, could someone tell me, if A and B could truthfully 00:13:08.390 --> 00:13:11.975 cooperate, what would be the optimal cooperative strategy? 00:13:15.320 --> 00:13:16.203 Yeah. 00:13:16.203 --> 00:13:18.921 AUDIENCE: You both go for a year. 00:13:18.921 --> 00:13:20.950 PROFESSOR: Right, you'd both be silent. 00:13:20.950 --> 00:13:24.780 So the optimal cooperative strategy is clear, which is to 00:13:24.780 --> 00:13:26.370 both be silent. 00:13:26.370 --> 00:13:28.350 So if the cop said, you know what, we'll let you guys get 00:13:28.350 --> 00:13:30.510 together and discuss what you want to do first-- 00:13:30.510 --> 00:13:32.450 which the cops would never be stupid enough to do-- but if 00:13:32.450 --> 00:13:35.170 they did and the guys can trust each other, then that's 00:13:35.170 --> 00:13:36.420 the optimal cooperative strategy. 00:13:40.500 --> 00:13:44.150 What we call optimal in the language of game theory, we 00:13:44.150 --> 00:13:45.555 call that the dominant strategy. 00:13:52.000 --> 00:13:57.720 A dominant strategy is the best thing to do no matter 00:13:57.720 --> 00:14:02.780 what the other guy does is the dominant strategy. 00:14:02.780 --> 00:14:05.150 So the dominant cooperative equilibrium strategy is to 00:14:05.150 --> 00:14:07.570 both stay quiet. 00:14:07.570 --> 00:14:12.950 But what's the dominant, non-cooperative strategy? 00:14:12.950 --> 00:14:15.045 What is the dominant non-cooperative strategy? 00:14:18.520 --> 00:14:20.960 So the ways with dominant strategy, we run through. 00:14:20.960 --> 00:14:23.830 Take prisoner A, ask the following. 00:14:23.830 --> 00:14:26.830 The dominant strategy is, is there a strategy that makes 00:14:26.830 --> 00:14:31.300 him better off regardless of what B does. 00:14:31.300 --> 00:14:33.410 Is there a strategy that makes A better off regardless of 00:14:33.410 --> 00:14:34.020 what B does. 00:14:34.020 --> 00:14:34.790 Let's go through. 00:14:34.790 --> 00:14:42.760 If A remains silent, if B remains silent he gets a year. 00:14:42.760 --> 00:14:46.180 If B talks he gets five years. 00:14:46.180 --> 00:14:50.780 Now compare that to prisoner A strategy of talking. 00:14:50.780 --> 00:14:54.870 Well if he talks he's better off than if he doesn't talk, 00:14:54.870 --> 00:14:57.470 if B's remaining silent. 00:14:57.470 --> 00:14:59.430 If he talks he's better off than if he 00:14:59.430 --> 00:15:01.980 doesn't talk if B talks. 00:15:01.980 --> 00:15:07.010 That is regardless of what B does, he's better off talking. 00:15:07.010 --> 00:15:10.210 Regardless of what B chooses to do, his dominant strategy 00:15:10.210 --> 00:15:11.380 is to talk. 00:15:11.380 --> 00:15:14.740 Because if B is silent, he's better off if he talks. 00:15:14.740 --> 00:15:17.310 If B talks he's better off if he talks. 00:15:17.310 --> 00:15:22.670 So matter what B chooses to do, A is better off talking. 00:15:22.670 --> 00:15:23.930 What about B? 00:15:23.930 --> 00:15:26.680 Well B, by the same logic, is always better 00:15:26.680 --> 00:15:28.210 off talking as well. 00:15:28.210 --> 00:15:30.590 No matter what A chooses to do, B is 00:15:30.590 --> 00:15:33.060 better off if he talks. 00:15:33.060 --> 00:15:34.580 So where do we end up? 00:15:34.580 --> 00:15:37.760 What ends up as the Nash equilibrium? 00:15:37.760 --> 00:15:41.750 The Nash equilibrium is that both prisoners talk. 00:15:41.750 --> 00:15:46.040 The dominant strategy for both prisoners is to talk. 00:15:46.040 --> 00:15:48.770 And they both end up worse off than they could have if they 00:15:48.770 --> 00:15:51.260 could have cooperated. 00:15:51.260 --> 00:15:54.710 So the dominant non-cooperative strategy is to 00:15:54.710 --> 00:16:01.930 both talk, even though if they could get together they'd be 00:16:01.930 --> 00:16:03.700 better both not talking. 00:16:03.700 --> 00:16:05.410 And this is basically how game theory works. 00:16:05.410 --> 00:16:07.010 Game theory math gets incredibly hard. 00:16:07.010 --> 00:16:09.370 And if you're interested, 14.12 is one of our most 00:16:09.370 --> 00:16:11.690 popular undergraduate courses, game theory. 00:16:11.690 --> 00:16:14.110 It's a great course where you take this and go run with it 00:16:14.110 --> 00:16:15.330 for a whole semester. 00:16:15.330 --> 00:16:17.360 It gets very complicated mathematically. 00:16:17.360 --> 00:16:19.690 But the basic idea in game theory is pretty 00:16:19.690 --> 00:16:23.090 straightforward, which is just ask, are there dominant 00:16:23.090 --> 00:16:25.780 strategies that can be played by each player. 00:16:25.780 --> 00:16:28.360 If each player has a dominant strategy and those dominant 00:16:28.360 --> 00:16:32.480 strategies lead to a Nash equilibrium then you're done. 00:16:32.480 --> 00:16:34.125 Here we're in a Nash equilibrium. 00:16:34.125 --> 00:16:36.040 Why are we in a Nash Equilibrium? 00:16:36.040 --> 00:16:41.730 Because given that A has talked, B's strategy, which is 00:16:41.730 --> 00:16:44.090 talking is the optimal thing to do. 00:16:44.090 --> 00:16:47.590 Given that B has talked, A's strategy which is talking is 00:16:47.590 --> 00:16:48.850 the optimal thing to do. 00:16:48.850 --> 00:16:51.600 So given what the other person's doing, each person is 00:16:51.600 --> 00:16:52.650 doing the right thing. 00:16:52.650 --> 00:16:55.660 So you're in Nash equilibrium. 00:16:55.660 --> 00:16:58.570 Given that B has chosen to talk, A is talking. 00:16:58.570 --> 00:17:01.560 That's the profit maximizing thing to do. 00:17:01.560 --> 00:17:03.030 Given that A is talking, B is talking. 00:17:03.030 --> 00:17:04.890 That's the profit maximizing thing to do. 00:17:04.890 --> 00:17:07.629 So given the strategy the other player's chosen that's 00:17:07.629 --> 00:17:08.380 an equilibrium. 00:17:08.380 --> 00:17:08.879 Yeah. 00:17:08.879 --> 00:17:12.871 AUDIENCE: If they both talk and got 10 years would that be 00:17:12.871 --> 00:17:14.368 the Nash equilibrium. 00:17:14.368 --> 00:17:17.869 PROFESSOR: No if they both talk, the 10 years only 00:17:17.869 --> 00:17:19.339 happens if one talks and the other one doesn't. 00:17:19.339 --> 00:17:21.331 AUDIENCE: No, I mean like, [INAUDIBLE]. 00:17:21.331 --> 00:17:23.849 PROFESSOR: Oh, if they both got 10 years? 00:17:23.849 --> 00:17:24.849 So let's ask that. 00:17:24.849 --> 00:17:26.099 Let's change this. 00:17:29.150 --> 00:17:31.470 Now let's just rework it. 00:17:31.470 --> 00:17:32.760 So now what's A's choice? 00:17:32.760 --> 00:17:36.920 Well A if he talks and B's silent, 00:17:36.920 --> 00:17:38.560 then he's better talking. 00:17:38.560 --> 00:17:41.480 But if he talks and B talks, he's worse talking. 00:17:41.480 --> 00:17:45.190 So then what he does depends on what B does. 00:17:45.190 --> 00:17:47.340 What B does is going to depend on what A does. 00:17:47.340 --> 00:17:50.870 And we can't obviously see the Nash equilibrium here. 00:17:50.870 --> 00:17:52.610 Because there's no dominant strategy. 00:17:52.610 --> 00:17:55.120 What you do depends on what the other person does. 00:17:55.120 --> 00:17:56.350 So there's no dominant strategy. 00:17:56.350 --> 00:17:59.350 Dominant strategies only occur if there's something that you 00:17:59.350 --> 00:18:01.720 should do no matter what the other person does. 00:18:01.720 --> 00:18:04.800 So in this case were these are both 2, there is a dominant 00:18:04.800 --> 00:18:06.880 strategy, It's to talk. 00:18:06.880 --> 00:18:09.280 If those are both 10 there's no longer a dominant strategy 00:18:09.280 --> 00:18:13.360 so we can't quickly get the Nash equilibrium. 00:18:13.360 --> 00:18:16.250 It's a good question. 00:18:16.250 --> 00:18:19.690 Now this is not just a cute example that you can use for 00:18:19.690 --> 00:18:22.590 prisoners, but actually explains firm 00:18:22.590 --> 00:18:24.270 behavior in many contexts. 00:18:24.270 --> 00:18:27.920 So the best example I like to think of of this is to think 00:18:27.920 --> 00:18:30.130 about advertising. 00:18:30.130 --> 00:18:32.950 So imagine if Coke and Pepsi, and imagine a world where 00:18:32.950 --> 00:18:34.360 Pepsi was as popular as Coke. 00:18:34.360 --> 00:18:35.090 That should never happen. 00:18:35.090 --> 00:18:35.960 Coke's way better. 00:18:35.960 --> 00:18:37.880 But imagine that was that world. 00:18:37.880 --> 00:18:41.480 So imagine a world where if there's no advertising then 00:18:41.480 --> 00:18:44.760 basically Pepsi and Coke would split the market 50-50. 00:18:44.760 --> 00:18:46.000 Imagine that set up. 00:18:46.000 --> 00:18:48.770 So if Pepsi and Coke could agree not to advertise they'd 00:18:48.770 --> 00:18:52.660 split the market 50-50. 00:18:52.660 --> 00:18:55.050 However, it's going to turn out that while that may be the 00:18:55.050 --> 00:18:58.280 dominant cooperative outcome, that's not the dominant 00:18:58.280 --> 00:19:01.310 non-cooperative outcome because each firm is better 00:19:01.310 --> 00:19:05.615 off advertising if the other one doesn't, or regardless. 00:19:05.615 --> 00:19:07.820 So for example, imagine the following payoffs matrix. 00:19:07.820 --> 00:19:09.330 I'm just making this up. 00:19:09.330 --> 00:19:13.800 But here you have Pepsi and here you have Coke. 00:19:13.800 --> 00:19:15.780 And imagine the payoff matrix. 00:19:15.780 --> 00:19:26.650 And the payoff matrix is if they don't advertise, so Pepsi 00:19:26.650 --> 00:19:29.435 can choose not to advertise, or it can advertise. 00:19:33.220 --> 00:19:36.910 So if they both don't advertise Pepsi gets 8 and 00:19:36.910 --> 00:19:37.510 Coke gets 8. 00:19:37.510 --> 00:19:38.110 I don't know what 8 is. 00:19:38.110 --> 00:19:39.230 8 is billion dollars. 00:19:39.230 --> 00:19:40.950 I'm just making up numbers here, doesn't matter. 00:19:40.950 --> 00:19:44.450 So $8 billion each. 00:19:44.450 --> 00:19:49.840 If they both do advertise then they still end up splitting 00:19:49.840 --> 00:19:50.320 the market. 00:19:50.320 --> 00:19:52.880 Because basically they're just as good as each other. 00:19:52.880 --> 00:19:54.510 So they both spend all the money advertising and just 00:19:54.510 --> 00:19:57.250 back up where they would have started, except they've wasted 00:19:57.250 --> 00:19:59.000 all this money in advertising. 00:19:59.000 --> 00:20:02.170 So if they both advertise they each earn $3 billion instead 00:20:02.170 --> 00:20:03.320 of $8 billion. 00:20:03.320 --> 00:20:04.410 That is, they each split the market. 00:20:04.410 --> 00:20:05.540 They end up back where they would have started but they 00:20:05.540 --> 00:20:08.760 pissed away a bunch of money advertising along the way. 00:20:08.760 --> 00:20:12.120 However if Coke advertised and Pepsi doesn't. 00:20:14.990 --> 00:20:16.696 Then almost everybody sees Coke, Coke, Coke everywhere 00:20:16.696 --> 00:20:17.440 and is like, Pepsi? 00:20:17.440 --> 00:20:19.320 Never heard of that. 00:20:19.320 --> 00:20:24.300 Coke makes $13 billion and Pepsi loses $2 billion. 00:20:24.300 --> 00:20:27.250 And likewise if Coke doesn't advertise but Pepsi does, 00:20:27.250 --> 00:20:28.230 people are like, I've never heard of Coke. 00:20:28.230 --> 00:20:30.270 I'm going to drink Pepsi. 00:20:30.270 --> 00:20:33.785 So Pepsi makes $13 billion and Coke makes minus $2 billion. 00:20:33.785 --> 00:20:36.550 Once again I just made numbers here so it would work, but 00:20:36.550 --> 00:20:40.360 these aren't real world examples. 00:20:40.360 --> 00:20:43.080 So once again we can see there is a dominant cooperative 00:20:43.080 --> 00:20:44.930 strategy, which is they both should 00:20:44.930 --> 00:20:48.150 agree let's not advertise. 00:20:48.150 --> 00:20:53.170 But if they can cooperate, then in fact what's the Nash 00:20:53.170 --> 00:20:53.700 equilibrium? 00:20:53.700 --> 00:20:54.840 Let's work it through. 00:20:54.840 --> 00:20:55.730 And there's no shortcuts here. 00:20:55.730 --> 00:20:56.670 You've just got to work this through. 00:20:56.670 --> 00:20:57.860 Let's look for Pepsi. 00:20:57.860 --> 00:21:01.450 Well Pepsi says if Coke doesn't advertise I'm better 00:21:01.450 --> 00:21:01.610 off advertising. 00:21:01.610 --> 00:21:02.860 If Coke does advertise, I'm better off advertising. 00:21:06.520 --> 00:21:09.240 So my dominant strategy is to advertise. 00:21:09.240 --> 00:21:14.980 Coke says, well gee, if Pepsi doesn't advertise I'm better 00:21:14.980 --> 00:21:15.530 off advertising. 00:21:15.530 --> 00:21:17.000 I make $13 billion instead of $8 billion. 00:21:17.000 --> 00:21:19.840 If Pepsi does advertise I make $3 billion instead of negative 00:21:19.840 --> 00:21:20.000 $2 billion. 00:21:20.000 --> 00:21:21.440 So I'm better off advertising too. 00:21:21.440 --> 00:21:24.060 So my dominant strategy is to advertise. 00:21:24.060 --> 00:21:26.960 So for both firms the dominant non-cooperative 00:21:26.960 --> 00:21:28.220 strategy is to advertise. 00:21:28.220 --> 00:21:32.110 So they both advertise and you end up in this equilibrium. 00:21:32.110 --> 00:21:36.380 It's an example of how a non-cooperative equilibrium 00:21:36.380 --> 00:21:39.680 can lead to what we call a race to the bottom. 00:21:39.680 --> 00:21:41.520 You can think of it as a race to the bottom. 00:21:41.520 --> 00:21:43.120 In other words, if they could cooperate they could just be 00:21:43.120 --> 00:21:43.550 better off. 00:21:43.550 --> 00:21:46.460 But because they can't trust the other, there's this race 00:21:46.460 --> 00:21:50.410 to the bottom where they both end up worse off. 00:21:50.410 --> 00:21:52.730 This is pretty striking. 00:21:52.730 --> 00:21:55.670 I thought they brought this out well in A Beautiful Mind, 00:21:55.670 --> 00:21:58.550 both the movie and the book, which is that all we've 00:21:58.550 --> 00:22:01.180 learned about economics so far is that 00:22:01.180 --> 00:22:03.520 competition is good, right? 00:22:03.520 --> 00:22:04.940 Competition is beneficial. 00:22:04.940 --> 00:22:07.190 Well here's a case, where in fact, at least in the firm's 00:22:07.190 --> 00:22:09.750 perspective, competition is bad. 00:22:09.750 --> 00:22:13.670 If they could just get together and cooperate they 00:22:13.670 --> 00:22:16.570 could make more money. 00:22:16.570 --> 00:22:21.470 Now, in fact, this example is not so far-fetched. 00:22:21.470 --> 00:22:22.810 I don't know when it started but it 00:22:22.810 --> 00:22:23.930 was during your lifetimes. 00:22:23.930 --> 00:22:30.460 When you were young, hard liquors, scotch, bourbon, 00:22:30.460 --> 00:22:34.290 whisky, et cetera, did not advertise on television. 00:22:34.290 --> 00:22:38.090 You never saw a Johnny Walker ad or anything on television 00:22:38.090 --> 00:22:39.690 until, I don't know when it changed maybe five 00:22:39.690 --> 00:22:41.250 or six years ago. 00:22:41.250 --> 00:22:42.150 Maybe 10 years ago, I don't know. 00:22:42.150 --> 00:22:43.860 But certainly in your lifetimes. 00:22:43.860 --> 00:22:45.250 That was not by government regulation. 00:22:45.250 --> 00:22:46.370 Many people thought there was a government 00:22:46.370 --> 00:22:47.210 regulation, they couldn't. 00:22:47.210 --> 00:22:48.060 That was not. 00:22:48.060 --> 00:22:50.470 That was a cooperative equilibrium where the makers 00:22:50.470 --> 00:22:53.500 of hard liquors got together and agreed not to advertise on 00:22:53.500 --> 00:22:55.800 TV. And they said it was in the "public interest" yada 00:22:55.800 --> 00:22:58.370 yada yada, but that wasn't. 00:22:58.370 --> 00:23:01.040 It was just they recognized the benefits of cooperating 00:23:01.040 --> 00:23:02.720 and not wasting money advertising on TV and 00:23:02.720 --> 00:23:04.020 competing with each other. 00:23:04.020 --> 00:23:06.990 Well that broke down some number of years ago. 00:23:06.990 --> 00:23:09.706 And now you see whiskey ads and scotch ads and other 00:23:09.706 --> 00:23:10.820 things on television. 00:23:10.820 --> 00:23:14.220 And they've moved to this non-cooperative equilibrium 00:23:14.220 --> 00:23:15.865 where they're all losing money by having this advertising. 00:23:21.080 --> 00:23:23.410 So that's in advertising. 00:23:23.410 --> 00:23:26.660 For me, once again, this is a hard thing, what intuition 00:23:26.660 --> 00:23:27.540 works for you. 00:23:27.540 --> 00:23:30.320 For me the intuition works best maybe from my scars from 00:23:30.320 --> 00:23:33.890 my dating life is thinking about personal decisions. 00:23:33.890 --> 00:23:36.970 So imagine that there's some girl named Allison. 00:23:36.970 --> 00:23:39.600 And Allison has a potential problem with her boyfriend. 00:23:39.600 --> 00:23:42.970 They've had a fight and now she's deciding whether or not 00:23:42.970 --> 00:23:46.010 to make up or break up. 00:23:46.010 --> 00:23:48.720 Now we can think of this just like Coke and Pepsi. 00:23:48.720 --> 00:23:51.070 Allison is going to be thinking, well gee, if he 00:23:51.070 --> 00:23:53.790 wants to make up with me and I want to make up with him then 00:23:53.790 --> 00:23:55.230 we're both better off. 00:23:55.230 --> 00:23:57.470 But if I want to make up with him and he doesn't want to 00:23:57.470 --> 00:24:00.920 make up with me, that makes me look like a total idiot. 00:24:00.920 --> 00:24:05.210 Whereas if I break up with him preemptively, yes it would be 00:24:05.210 --> 00:24:08.040 sad if he wanted to stay with me, but at least if he wanted 00:24:08.040 --> 00:24:10.150 to break up with me I look better. 00:24:10.150 --> 00:24:12.880 So she preemptively breaks up with him. 00:24:12.880 --> 00:24:16.550 John, her boyfriend, thinking the same thing, behaves in 00:24:16.550 --> 00:24:17.970 exactly the same way. 00:24:17.970 --> 00:24:20.940 So it could be that even though they both would be 00:24:20.940 --> 00:24:23.890 better off if they just said, look the honest truth is, 00:24:23.890 --> 00:24:26.470 we're both wrong, let's make up and we'll both be happy. 00:24:26.470 --> 00:24:28.590 Because they're so afraid of being the one being dumped, 00:24:28.590 --> 00:24:30.740 they end up breaking up. 00:24:30.740 --> 00:24:33.560 Now we all know of examples like this from life, where 00:24:33.560 --> 00:24:36.720 people stupidly if they could have just cooperated had a 00:24:36.720 --> 00:24:38.830 better outcome because they're so afraid of being left with 00:24:38.830 --> 00:24:40.740 the short end of the stick, because they don't cooperate 00:24:40.740 --> 00:24:42.780 you end up with the worst outcome for both. 00:24:42.780 --> 00:24:44.310 That's an example of a non-cooperative 00:24:44.310 --> 00:24:48.090 equilibrium in real life. 00:24:48.090 --> 00:24:53.610 Now in real life there is one aspect of oligopolistic 00:24:53.610 --> 00:24:58.240 non-cooperative equilibria that allow them to be 00:24:58.240 --> 00:24:59.000 enforced, however. 00:24:59.000 --> 00:25:01.790 That allow you to overcome the prisoner's dilemma. 00:25:01.790 --> 00:25:03.470 There's one thing that allows you to overcome the prisoner's 00:25:03.470 --> 00:25:06.225 dilemma and that's repeated games. 00:25:14.550 --> 00:25:16.890 Repeated games can help you overcome 00:25:16.890 --> 00:25:18.140 the prisoner's dilemma. 00:25:20.920 --> 00:25:25.420 Now let's take the Coke and Pepsi example and let's 00:25:25.420 --> 00:25:28.830 imagine that they're making the advertising 00:25:28.830 --> 00:25:29.840 decision every period. 00:25:29.840 --> 00:25:30.590 Every period they have to make an 00:25:30.590 --> 00:25:32.730 independent advertising decision. 00:25:32.730 --> 00:25:36.240 They can advertise or not advertise every period. 00:25:36.240 --> 00:25:39.170 And imagine Coke says to Pepsi, I've got the following 00:25:39.170 --> 00:25:41.060 deal for you. 00:25:41.060 --> 00:25:47.210 I commit to not advertise as long as you don't, but the 00:25:47.210 --> 00:25:51.540 minute you advertise I'm going to advertise forever. 00:25:51.540 --> 00:25:54.310 So as long as you don't advertise I won't. 00:25:54.310 --> 00:25:56.900 But if you ever run an ad, the bet's off and I'm never going 00:25:56.900 --> 00:25:57.720 to cooperate with you. 00:25:57.720 --> 00:26:00.400 I'm going to advertise forever. 00:26:00.400 --> 00:26:04.310 Let's think about Pepsi's choice in period one if Coke 00:26:04.310 --> 00:26:05.190 presents them with this deal. 00:26:05.190 --> 00:26:06.930 Let's think about Pepsi's choice if Coke presents them 00:26:06.930 --> 00:26:09.180 with this deal. 00:26:09.180 --> 00:26:12.450 Well one thing is they could say, ha ha, great Coke, good 00:26:12.450 --> 00:26:13.210 job trusting me. 00:26:13.210 --> 00:26:15.560 I'm going to screw you in advertising period one. 00:26:15.560 --> 00:26:18.130 So Pepsi could say, great, Coke's laid down arms in 00:26:18.130 --> 00:26:19.170 period one. 00:26:19.170 --> 00:26:20.460 I'm going to go and advertise. 00:26:20.460 --> 00:26:22.250 I'll make $13 billion in period one because Coke's 00:26:22.250 --> 00:26:23.210 wimped out. 00:26:23.210 --> 00:26:26.160 And then I'll make $3 billion forever after, because forever 00:26:26.160 --> 00:26:27.400 after we're both going to advertise. 00:26:27.400 --> 00:26:30.400 But at least I' beat them up that first period. 00:26:30.400 --> 00:26:33.570 However, if Pepsi says, wait a second, if Coke's really 00:26:33.570 --> 00:26:36.930 right, honest, then I can get an equilibrium where we make 00:26:36.930 --> 00:26:38.780 $8 billion forever. 00:26:38.780 --> 00:26:40.790 And certainly $8 billion forever a better deal than $13 00:26:40.790 --> 00:26:43.330 billion one year and $3 billion forever. 00:26:43.330 --> 00:26:47.560 So in fact if Coke's willing to live up to that promise 00:26:47.560 --> 00:26:49.000 then that is a good deal. 00:26:49.000 --> 00:26:51.360 And actually we can turn this non-cooperative equilibrium 00:26:51.360 --> 00:26:53.770 into a cooperative equilibrium through the enforcement of a 00:26:53.770 --> 00:26:55.570 repeated game. 00:26:55.570 --> 00:26:57.650 Through the fact that this game gets played over and over 00:26:57.650 --> 00:27:05.940 and over again you can enforce a cooperative equilibrium. 00:27:05.940 --> 00:27:07.970 We can come back to relationships again. 00:27:07.970 --> 00:27:10.910 If you're in a committed relationship and you know that 00:27:10.910 --> 00:27:13.020 if I say it's your fault over and over again, eventually 00:27:13.020 --> 00:27:16.230 person's going to leave. Then people say gee, I'm willing to 00:27:16.230 --> 00:27:18.460 take some of the blame and not always say it's your fault and 00:27:18.460 --> 00:27:19.620 we have a fight. 00:27:19.620 --> 00:27:21.230 Because I know that if I always say it's your fault 00:27:21.230 --> 00:27:22.740 ultimately that will break the relationship up and that makes 00:27:22.740 --> 00:27:26.180 me worse off then admitting it was my fault some of the time. 00:27:26.180 --> 00:27:27.470 It's the same logic. 00:27:27.470 --> 00:27:27.860 Yeah. 00:27:27.860 --> 00:27:30.480 AUDIENCE: Is the point of the game to make more than the 00:27:30.480 --> 00:27:31.510 other guy or to make as much as possible? 00:27:31.510 --> 00:27:34.580 PROFESSOR: Make as much as possible. 00:27:34.580 --> 00:27:35.530 That's a good point. 00:27:35.530 --> 00:27:39.570 I presume that the point is to make as much as possible. 00:27:39.570 --> 00:27:41.850 I'm ruling out cut off your nose to spite your face 00:27:41.850 --> 00:27:42.920 equilibria. 00:27:42.920 --> 00:27:45.230 So in other words, I'm assuming the goals is to 00:27:45.230 --> 00:27:48.050 maximize profits not relevant mark position. 00:27:48.050 --> 00:27:48.830 That's a good point. 00:27:48.830 --> 00:27:49.920 I should have made that assumption clear. 00:27:49.920 --> 00:27:54.000 It's the assumption we're always making whatever we 00:27:54.000 --> 00:27:58.270 confirm behavior is assuming it's profit maximization. 00:27:58.270 --> 00:28:03.280 So repeated games can enforce a cooperative equilibria, 00:28:03.280 --> 00:28:04.080 essentially. 00:28:04.080 --> 00:28:06.550 Even in a non-cooperative set up. 00:28:06.550 --> 00:28:10.570 But it turns out this only works if the 00:28:10.570 --> 00:28:11.820 game goes on forever. 00:28:14.060 --> 00:28:16.440 This only works if the game is going to go on forever. 00:28:16.440 --> 00:28:22.450 So, for example, imagine that Pepsi knows that in 10 years 00:28:22.450 --> 00:28:24.380 the US government is going to ban the advertisement of 00:28:24.380 --> 00:28:26.080 sugared sodas. 00:28:26.080 --> 00:28:27.640 The US government is going to finally say, look, people are 00:28:27.640 --> 00:28:30.040 too obese, no more advertising sugary sodas. 00:28:30.040 --> 00:28:31.710 Pepsi knows this. 00:28:31.710 --> 00:28:33.590 In 10 years that's going to happen. 00:28:33.590 --> 00:28:36.270 Well Pepsi's thinking, gee, that means in 00:28:36.270 --> 00:28:39.790 year 10 I should advertise. 00:28:39.790 --> 00:28:41.580 In that last year I should advertise because Coke can't 00:28:41.580 --> 00:28:43.160 punish me the next year because no one can advertise 00:28:43.160 --> 00:28:44.340 the next year. 00:28:44.340 --> 00:28:46.410 So I know starting after 10 years we're both in this 00:28:46.410 --> 00:28:47.960 equilibrium because the government's 00:28:47.960 --> 00:28:48.900 going to enforce it. 00:28:48.900 --> 00:28:52.070 So in ninth year, right beforehand, right before that 00:28:52.070 --> 00:28:56.080 government ban I should advertise and Coke can't get 00:28:56.080 --> 00:28:57.480 me the next period because they don't have the 00:28:57.480 --> 00:28:59.140 tool to punish me. 00:28:59.140 --> 00:29:00.980 Well Coke, of course, knows Pepsi is going 00:29:00.980 --> 00:29:02.680 to behave that way. 00:29:02.680 --> 00:29:04.430 So Coke says, wait a second, if Pepsi's going to behave 00:29:04.430 --> 00:29:06.680 that way then I better advertise in the ninth period 00:29:06.680 --> 00:29:09.540 too or I'm going to get hit with a minus $2 billion. 00:29:09.540 --> 00:29:12.480 So I'm going to advertise in the ninth period too. 00:29:12.480 --> 00:29:14.305 Well Pepsi says, look, if Coke's going to advertise in 00:29:14.305 --> 00:29:15.600 the ninth period for sure, I may as well advertise in the 00:29:15.600 --> 00:29:18.170 eight period because Coke's going to advertise in the 00:29:18.170 --> 00:29:18.980 ninth period for sure. 00:29:18.980 --> 00:29:20.910 And by the same logic you can work it back that they'll both 00:29:20.910 --> 00:29:22.220 advertise right away and you'll end up with a 00:29:22.220 --> 00:29:24.300 non-cooperative equilibrium. 00:29:24.300 --> 00:29:29.290 That is a repeated game that does not enforce the 00:29:29.290 --> 00:29:30.700 cooperative equilibrium. 00:29:30.700 --> 00:29:34.260 Because by working that logic backwards if it ends in some 00:29:34.260 --> 00:29:37.230 realistic time frame, then you better off just breaking it 00:29:37.230 --> 00:29:39.060 now rather waiting for that period where 00:29:39.060 --> 00:29:40.670 you're the one who loses. 00:29:40.670 --> 00:29:41.080 Yeah. 00:29:41.080 --> 00:29:44.050 AUDIENCE: [INAUDIBLE] 00:29:44.050 --> 00:29:46.030 what if Pepsi [INAUDIBLE]? 00:29:46.030 --> 00:29:47.290 PROFESSOR: Exactly. 00:29:47.290 --> 00:29:50.400 If they don't then you could imagine that if Pepsi knows 00:29:50.400 --> 00:29:53.583 this and Coke doesn't, then Pepsi's optimal strategy will 00:29:53.583 --> 00:29:55.810 be to cooperate to the next to last period then go ahead and 00:29:55.810 --> 00:29:57.480 screw Coke and then Coke will lose. 00:29:57.480 --> 00:30:01.020 But presuming symmetric information, repeated games 00:30:01.020 --> 00:30:04.890 cannot enforce these equilibria if they end. 00:30:04.890 --> 00:30:10.930 So this is just an incredibly quick introduction to the fun 00:30:10.930 --> 00:30:13.530 that is game theory. 00:30:13.530 --> 00:30:16.510 We're going to go on now and do more rigorous versions of 00:30:16.510 --> 00:30:17.460 these models. 00:30:17.460 --> 00:30:20.125 But this is just to get you excited about the tools you 00:30:20.125 --> 00:30:22.270 can do with game theory with fun examples. 00:30:22.270 --> 00:30:23.880 Game theory is about taking these fun examples and 00:30:23.880 --> 00:30:25.190 thinking a lot harder about a lot. 00:30:25.190 --> 00:30:28.320 What if there's asymmetric information? 00:30:28.320 --> 00:30:31.905 What if the game ends long enough in the future that 00:30:31.905 --> 00:30:33.000 you're willing to be patient? 00:30:33.000 --> 00:30:35.270 How far off in the future does the game have to end to still 00:30:35.270 --> 00:30:36.700 enforce the cooperate equilibrium? 00:30:36.700 --> 00:30:38.270 What if there are three players? 00:30:38.270 --> 00:30:40.680 What if players move in different orders? 00:30:40.680 --> 00:30:42.440 What if one player goes first, the second player responds to 00:30:42.440 --> 00:30:44.670 that, is it different than if they go simultaneously? 00:30:44.670 --> 00:30:46.690 These are all really interesting issues that are 00:30:46.690 --> 00:30:49.060 very relevant to the real world firm behavior that you 00:30:49.060 --> 00:30:50.090 learn about game theory. 00:30:50.090 --> 00:30:53.890 So this is just to whet your appetite for that. 00:30:53.890 --> 00:30:57.190 Having done that we're going to now turn, leave aside these 00:30:57.190 --> 00:30:59.430 more interesting dynamic issues and focus on a specific 00:30:59.430 --> 00:31:04.120 example of a non-cooperative oligopoly. 00:31:04.120 --> 00:31:07.400 Because, once again, this is all fun intuitively, but we 00:31:07.400 --> 00:31:09.620 want you to be able to work through a problem. 00:31:09.620 --> 00:31:10.902 And the way to work that through is we're going to have 00:31:10.902 --> 00:31:14.290 to move to a specific, simplified example. 00:31:14.290 --> 00:31:16.280 And the example we're going to focus on is 00:31:16.280 --> 00:31:18.070 called the Cournot model. 00:31:21.490 --> 00:31:27.695 The Cournot model of non-cooperative oligopoly. 00:31:30.900 --> 00:31:34.340 The way we're going to do this here, is we're going to return 00:31:34.340 --> 00:31:38.320 to the example we had with the prisoner's dilemma. 00:31:38.320 --> 00:31:41.350 But instead of just facing two choices, talk or not talk, 00:31:41.350 --> 00:31:43.770 we're going to talk about firms facing a whole continuum 00:31:43.770 --> 00:31:44.750 of choices. 00:31:44.750 --> 00:31:49.040 Firms choosing how much they produce in a non-cooperative 00:31:49.040 --> 00:31:51.550 equilibria situation. 00:31:51.550 --> 00:31:53.420 So, for example, let's take the example 00:31:53.420 --> 00:31:54.500 they use in the book. 00:31:54.500 --> 00:31:58.160 Let's imagine there's two airlines that fly between New 00:31:58.160 --> 00:32:00.590 York and Chicago, American and United. 00:32:00.590 --> 00:32:02.230 And let's imagine for simplicity those are the only 00:32:02.230 --> 00:32:02.830 two airlines. 00:32:02.830 --> 00:32:04.680 Because of the hub and spoke system we talked about last 00:32:04.680 --> 00:32:09.270 time, let's say all the gates in Chicago that are available 00:32:09.270 --> 00:32:11.130 to come from New York are taken by two airlines-- 00:32:11.130 --> 00:32:12.260 United and American. 00:32:12.260 --> 00:32:14.170 Those are your only two options 00:32:14.170 --> 00:32:17.440 flying New York to Chicago. 00:32:17.440 --> 00:32:20.920 And the question we want to ask is, get in that world, how 00:32:20.920 --> 00:32:23.890 do United and American decide how many flights to run and 00:32:23.890 --> 00:32:26.690 what price to charge? 00:32:26.690 --> 00:32:27.980 If they're monopolies we'd know. 00:32:27.980 --> 00:32:29.195 If it was a perfect competition we'd know, but how 00:32:29.195 --> 00:32:30.445 do they decide this all oligopolistic. 00:32:35.650 --> 00:32:38.630 The way we figure this out is by looking for the Nash 00:32:38.630 --> 00:32:40.520 equilibrium in this case, which we also call Cournot 00:32:40.520 --> 00:32:43.240 equilibrium. 00:32:43.240 --> 00:32:53.770 Which is basically the quantity is chosen by each 00:32:53.770 --> 00:33:02.490 firm such that holding all other 00:33:02.490 --> 00:33:03.740 firms' quantities constant. 00:33:11.670 --> 00:33:15.320 So each firm chooses quantity such that holding all other 00:33:15.320 --> 00:33:19.545 firm's quantities constant they are maximizing profits. 00:33:24.750 --> 00:33:28.270 So I choose a quantity such that holding all the other 00:33:28.270 --> 00:33:31.470 firm's quantities constant I'm choosing a 00:33:31.470 --> 00:33:32.940 profit-maximizing quantity. 00:33:36.740 --> 00:33:42.360 And if each firm can choose a quantity that makes the market 00:33:42.360 --> 00:33:45.510 function where this is met, then you're in Cournot 00:33:45.510 --> 00:33:47.450 equilibrium. 00:33:47.450 --> 00:33:49.310 You're in Cournot equilibrium when each firm has 00:33:49.310 --> 00:33:50.780 decided, I'm happy. 00:33:50.780 --> 00:33:52.290 It's the same as the Nash concept. 00:33:52.290 --> 00:33:56.480 I'm happy with what I'm producing given what everybody 00:33:56.480 --> 00:33:57.410 else is producing. 00:33:57.410 --> 00:34:00.030 If everybody feels that way then you're in a Nash 00:34:00.030 --> 00:34:03.220 equilibrium or a Cournot equilibrium. 00:34:03.220 --> 00:34:06.460 So to see this, this is not immediately intuitive. 00:34:06.460 --> 00:34:07.900 Let me just talk you through the steps of how 00:34:07.900 --> 00:34:09.860 you'd solve for this. 00:34:09.860 --> 00:34:11.789 How do you actually solve for a Cournot equilibrium? 00:34:16.370 --> 00:34:18.560 So basically what are the steps to solving? 00:34:18.560 --> 00:34:24.400 Step one for solving a Cournot equilibrium is to create each 00:34:24.400 --> 00:34:25.900 firm's residual demand. 00:34:25.900 --> 00:34:28.800 So compute residual demand. 00:34:28.800 --> 00:34:32.909 We talked about residual demand curves earlier. 00:34:32.909 --> 00:34:36.940 Which is, that's the demand for my firm given the quantity 00:34:36.940 --> 00:34:39.300 absorbed by other firms in the market. 00:34:39.300 --> 00:34:41.159 In this case it's quantities absorbed by the one other firm 00:34:41.159 --> 00:34:42.699 in the market, but in general you do this 00:34:42.699 --> 00:34:44.050 with multiple players. 00:34:44.050 --> 00:34:45.689 So first you calculate residual demand. 00:34:49.909 --> 00:34:58.660 Then having computed your residual demand you develop a 00:34:58.660 --> 00:35:00.660 marginal revenue function. 00:35:00.660 --> 00:35:03.710 You calculate your marginal revenue which will be a 00:35:03.710 --> 00:35:08.020 function of other firm's quantities. 00:35:12.080 --> 00:35:14.740 So your residual demand will lead you to calculate a 00:35:14.740 --> 00:35:15.750 marginal revenue function. 00:35:15.750 --> 00:35:17.370 It's a function of other firms' quantities. 00:35:20.550 --> 00:35:29.860 You then do the same, do one and two for all firms. So for 00:35:29.860 --> 00:35:31.960 each firm you end up with a marginal revenue function and 00:35:31.960 --> 00:35:33.330 a function of all the firm's quantities. 00:35:36.470 --> 00:35:40.230 Step four is you have n equations and n 00:35:40.230 --> 00:35:41.615 unknowns and you solve. 00:35:47.610 --> 00:35:50.520 So you develop a series of equation where each firm's 00:35:50.520 --> 00:35:53.290 marginal revenue function is a function of each other firms 00:35:53.290 --> 00:35:54.540 quantities. 00:35:54.540 --> 00:35:57.230 You get one equation like that for each firm. 00:35:57.230 --> 00:35:59.640 That leaves you n equations and n unknowns you solve. 00:35:59.640 --> 00:36:02.370 If you can solve it then you reach equilibrium. 00:36:02.370 --> 00:36:04.710 If you don't have a solution then there is no stable Nash 00:36:04.710 --> 00:36:05.210 equilibrium. 00:36:05.210 --> 00:36:08.400 But if you can solve that there is a Cournot equilibrium 00:36:08.400 --> 00:36:10.400 and you solve for it. 00:36:10.400 --> 00:36:12.780 So what we're going to do here is I'm going to illustrate 00:36:12.780 --> 00:36:16.420 this to you graphically today and we'll work through some 00:36:16.420 --> 00:36:19.250 more of the math of it next time. 00:36:19.250 --> 00:36:22.780 So we'll start by doing this graphically. 00:36:22.780 --> 00:36:27.410 So let's start by considering the case of American Airlines. 00:36:27.410 --> 00:36:30.660 Let's start with figure 16-1. 00:36:30.660 --> 00:36:32.485 Start by considering the case of American Airlines. 00:36:36.580 --> 00:36:43.440 And let's say that the demand curve in this market in our 00:36:43.440 --> 00:36:48.590 example we're going to do, let's say that the demand 00:36:48.590 --> 00:36:54.320 curve is of the form p equals 339 minus q. 00:36:54.320 --> 00:36:59.570 So there's 339,000 flights that are demanded each month. 00:36:59.570 --> 00:37:03.140 Each month there are 339,000 flights demanded 00:37:03.140 --> 00:37:04.920 in the whole market. 00:37:04.920 --> 00:37:06.660 So 339,000 people want to go from New York to 00:37:06.660 --> 00:37:09.890 Chicago every month. 00:37:09.890 --> 00:37:16.080 And let's also assume the marginal cost is $147. 00:37:16.080 --> 00:37:17.790 I don't know where Perloff came up with these numbers, 00:37:17.790 --> 00:37:19.460 but let's just go with them. 00:37:19.460 --> 00:37:20.740 The specific numbers don't matter. 00:37:23.260 --> 00:37:26.470 Now what would American Airlines do if it was a 00:37:26.470 --> 00:37:28.180 monopolist? 00:37:28.180 --> 00:37:31.540 If American Airlines was a monopolist, it would set 00:37:31.540 --> 00:37:38.470 marginal revenues which are 339 minus 2q by the same math 00:37:38.470 --> 00:37:39.040 we did before. 00:37:39.040 --> 00:37:41.670 You just multiply it through by q and then differentiate 00:37:41.670 --> 00:37:45.020 and you get 339 minus 2q equal to the marginal 00:37:45.020 --> 00:37:49.850 cost which is 147. 00:37:49.850 --> 00:38:00.180 So if it was a monopolist it would choose a quantity of 96 00:38:00.180 --> 00:38:07.644 and it would choose a price of $243. 00:38:07.644 --> 00:38:10.020 A prices of $243 which we would just get 00:38:10.020 --> 00:38:11.150 out the demand curve. 00:38:11.150 --> 00:38:14.780 If the quantity is 96, the price is $243. 00:38:14.780 --> 00:38:17.830 And that's what we see here. 00:38:17.830 --> 00:38:20.820 The marginal revenue curve intersects the marginal cost 00:38:20.820 --> 00:38:26.270 curve at a quantity of 96,000. 00:38:26.270 --> 00:38:28.540 You then go up to the demand curve to read off the price. 00:38:28.540 --> 00:38:29.940 Remember for a monopolist you've got to still respect 00:38:29.940 --> 00:38:31.350 the demand curve. 00:38:31.350 --> 00:38:32.585 You get the demand curve to read off the 00:38:32.585 --> 00:38:34.210 price, that's $243. 00:38:34.210 --> 00:38:36.560 That's what American would do if they were monopolist. So if 00:38:36.560 --> 00:38:40.350 they were the only folks flying New York to Chicago, 00:38:40.350 --> 00:38:47.480 they fly 96,000 people a month at a price of $243,000. 00:38:47.480 --> 00:38:50.360 However, now let's say American recognizes that 00:38:50.360 --> 00:38:51.970 United is in the market. 00:38:51.970 --> 00:38:55.910 And let's say American recognizes that United is 00:38:55.910 --> 00:38:58.490 going to deliver some amount of flights q sub u. 00:39:01.390 --> 00:39:02.675 They know American is going to do some amount of 00:39:02.675 --> 00:39:03.510 flights q sub u. 00:39:03.510 --> 00:39:06.150 They don't quite know yet what it is, but they know there's 00:39:06.150 --> 00:39:07.400 going to be some amount of flights q sub u. 00:39:10.220 --> 00:39:14.640 So the residual demand for American is q sub a equals 00:39:14.640 --> 00:39:17.130 total demand minus q sub u. 00:39:17.130 --> 00:39:18.480 That's their residual demand. 00:39:22.240 --> 00:39:27.370 So, for example, let's say that American just guesses 00:39:27.370 --> 00:39:31.140 that United will fly 64,000 passengers. 00:39:31.140 --> 00:39:34.050 Let's say Americans says, look, I just know, I've got 00:39:34.050 --> 00:39:39.230 some corporate spy who's told me that United will fly 64,000 00:39:39.230 --> 00:39:41.830 passengers. 00:39:41.830 --> 00:39:44.370 So what you want to do is then you just re-solve the problem 00:39:44.370 --> 00:39:46.300 but using residual demand. 00:39:46.300 --> 00:39:48.490 So then you say, well if United is going to fly 64,000 00:39:48.490 --> 00:39:53.810 passengers then my residual demand is that price equals 00:39:53.810 --> 00:40:03.000 339 minus the quantity I sell, q sub a, minus q sub u, which 00:40:03.000 --> 00:40:06.400 I think is 64,000, which is 64. 00:40:06.400 --> 00:40:17.600 So my new residual demand is p equals 275 minus q sub a. 00:40:17.600 --> 00:40:18.720 That's my new residual demand. 00:40:18.720 --> 00:40:21.110 Because I thought United is going to sell 64,000. 00:40:21.110 --> 00:40:23.520 So instead of my demand being 339 minus q, now 00:40:23.520 --> 00:40:26.520 275 minus q sub a. 00:40:26.520 --> 00:40:28.970 That's what's left. 00:40:28.970 --> 00:40:34.270 So if I use this as my new demand function and re-solve, 00:40:34.270 --> 00:40:37.700 if this is my demand function, my marginal revenues are then 00:40:37.700 --> 00:40:42.150 275 minus 2 qa. 00:40:42.150 --> 00:40:47.010 My marginal cost is the same which is 147. 00:40:47.010 --> 00:40:52.530 So instead of my equation being 339 minus 2q equals 147. 00:40:52.530 --> 00:40:57.180 Now it's 275 minus 2qa equals 147. 00:40:57.180 --> 00:41:06.790 If I do that I'm going to get a qa star of 64,000 flights. 00:41:06.790 --> 00:41:10.150 I'm going to say, well look, if I was a monopolist I would 00:41:10.150 --> 00:41:12.140 have deliver 96,000 flights. 00:41:12.140 --> 00:41:16.560 But given that United is delivering 64,000, that's it's 00:41:16.560 --> 00:41:20.030 going to be optimal for me to also deliver 64,000. 00:41:20.030 --> 00:41:23.235 At 64,000 flights what's my price going to be? 00:41:23.235 --> 00:41:25.730 Well my price is 275 minus qa. 00:41:25.730 --> 00:41:31.530 So my price is going be to be $211. 00:41:31.530 --> 00:41:34.285 If I think United is delivering 64,000 flights then 00:41:34.285 --> 00:41:41.040 I'm going to deliver 64,000 flights at a price of $211. 00:41:41.040 --> 00:41:46.110 So that's basically how American would function. 00:41:46.110 --> 00:41:48.440 Now what's strange about this is American doesn't know how 00:41:48.440 --> 00:41:50.090 many flights United is going to deliver. 00:41:50.090 --> 00:41:50.890 There isn't such a thing. 00:41:50.890 --> 00:41:53.910 In fact, it's not like there's not some rule which says we're 00:41:53.910 --> 00:41:55.390 going to go 64,000. 00:41:55.390 --> 00:41:58.530 United is trying to figure this out too. 00:41:58.530 --> 00:42:02.730 So, in fact, simultaneously to American making this decision, 00:42:02.730 --> 00:42:05.210 United is making the same decision. 00:42:05.210 --> 00:42:08.180 And they're going through the exact same math. 00:42:08.180 --> 00:42:11.140 They're saying, well gee, given how much American flies, 00:42:11.140 --> 00:42:12.390 how much should we fly? 00:42:15.040 --> 00:42:16.620 They're going through the same math. 00:42:16.620 --> 00:42:23.500 And in fact if we assume that both firms have to face the 00:42:23.500 --> 00:42:26.600 same marginal cost and the same demand curve, then in 00:42:26.600 --> 00:42:29.970 fact they're solving a symmetric problem. 00:42:29.970 --> 00:42:32.380 They are also creating a residual demand function, but 00:42:32.380 --> 00:42:36.310 instead of being qa equals d minus qu, now United is making 00:42:36.310 --> 00:42:38.850 qu equals d minus qa. 00:42:38.850 --> 00:42:41.580 They're making a parallel residual demand function and 00:42:41.580 --> 00:42:44.110 they are solving as well. 00:42:44.110 --> 00:42:48.600 And both firms, therefore, are ending up with choices of 00:42:48.600 --> 00:42:53.310 quantities that depend on the other firm's quantity. 00:42:53.310 --> 00:43:00.300 And in particular what they're developing is what we call a 00:43:00.300 --> 00:43:01.830 best response curve. 00:43:01.830 --> 00:43:04.980 So figure 16-2, I skipped over figure 16-2. 00:43:04.980 --> 00:43:10.520 This just illustrates what happens when American thinks 00:43:10.520 --> 00:43:11.560 United is committing 64,000. 00:43:11.560 --> 00:43:13.060 Let's go through that in one second. 00:43:13.060 --> 00:43:15.720 Get through it mathematically. 00:43:15.720 --> 00:43:17.630 This is an example where American knows United is doing 00:43:17.630 --> 00:43:19.390 64,000 flights. 00:43:19.390 --> 00:43:21.860 So they say, well look, my residual demand is essentially 00:43:21.860 --> 00:43:24.500 this new line d super r. 00:43:24.500 --> 00:43:27.420 And that's what I choose on that new line. 00:43:27.420 --> 00:43:31.560 So that creates a new marginal revenue curve, mr super r. 00:43:31.560 --> 00:43:34.290 That new marginal revenue curve intersects marginal cost 00:43:34.290 --> 00:43:38.250 at 64,000 and that's why I fly only 64,000 flights 00:43:38.250 --> 00:43:40.380 at a price of $211. 00:43:40.380 --> 00:43:44.395 So you see here is one example of how given an amount United 00:43:44.395 --> 00:43:48.760 is flying, how American chooses how much to fly. 00:43:48.760 --> 00:43:53.140 Questions about that graphic that ties the math I did here? 00:43:53.140 --> 00:43:56.410 What figure 16-3 does is say, look, we can actually do this 00:43:56.410 --> 00:43:59.240 for a whole host of possible production levels 00:43:59.240 --> 00:44:00.770 by the other firm. 00:44:00.770 --> 00:44:05.880 And we can develop what we call best response curves. 00:44:05.880 --> 00:44:09.160 Best response curves are, given what the other firm 00:44:09.160 --> 00:44:11.290 does, what should I do. 00:44:11.290 --> 00:44:17.140 So, for example, American's best response curve is given 00:44:17.140 --> 00:44:22.190 that-- so on the x-axis we have how many thousands of 00:44:22.190 --> 00:44:27.180 flights American's passengers are flying per quarter. 00:44:27.180 --> 00:44:29.290 On the y-axis how many thousands of flights United 00:44:29.290 --> 00:44:33.560 passengers are flying per quarter. 00:44:33.560 --> 00:44:44.770 So, for example, if American decides to fly zero flights 00:44:44.770 --> 00:44:48.410 then United should fly 96 flights, right? 00:44:48.410 --> 00:44:51.280 Then United is a monopolist. So that's the point on the 00:44:51.280 --> 00:44:55.150 y-axis, to 96,0 point on the curve. 00:44:55.150 --> 00:44:57.600 With a 0 on the x-axis, 96 on the y-axis. 00:44:57.600 --> 00:45:00.350 If American decides to fly 0. 00:45:00.350 --> 00:45:01.580 United should fly 96. 00:45:01.580 --> 00:45:04.070 That's the monopoly case we just solved. 00:45:04.070 --> 00:45:09.040 If American decides to fly 64, United should fly 64. 00:45:09.040 --> 00:45:11.710 That's the case we just solved as well. 00:45:11.710 --> 00:45:14.355 Likewise, American's best response curve is 00:45:14.355 --> 00:45:15.540 this steeper line. 00:45:15.540 --> 00:45:16.730 But it's the same thing. 00:45:16.730 --> 00:45:20.790 If United flies 0, American should fly 96 then at 0 on the 00:45:20.790 --> 00:45:23.110 y-axis, 96 on the x-axis. 00:45:23.110 --> 00:45:28.040 So if United flies 0 American should fly 96. 00:45:28.040 --> 00:45:31.770 If United flies 64, American should fly 64. 00:45:31.770 --> 00:45:35.680 So you can actually, literally trace out these curves asking 00:45:35.680 --> 00:45:38.770 at every single point, given what the other guy's doing, 00:45:38.770 --> 00:45:41.020 what should I do. 00:45:41.020 --> 00:45:43.410 So we solved for two points on this curve. 00:45:43.410 --> 00:45:46.570 We solved for the other guy producing zero point, which is 00:45:46.570 --> 00:45:48.250 you produce 96. 00:45:48.250 --> 00:45:50.470 We solved for the other guy producing 64 point which is 00:45:50.470 --> 00:45:51.820 you produce 64. 00:45:51.820 --> 00:45:53.540 That same math can be used to solve for every 00:45:53.540 --> 00:45:55.300 point on this curve. 00:45:55.300 --> 00:45:55.780 Yeah? 00:45:55.780 --> 00:45:56.750 AUDIENCE: [INAUDIBLE] 00:45:56.750 --> 00:45:57.235 192 point. 00:45:57.235 --> 00:46:00.330 PROFESSOR: The 192 point is it's the 00:46:00.330 --> 00:46:01.630 question is the following. 00:46:01.630 --> 00:46:08.560 At what point would American produce zero. 00:46:08.560 --> 00:46:10.855 How much when United have to produce for American to 00:46:10.855 --> 00:46:11.540 produce zero. 00:46:11.540 --> 00:46:12.630 Well they'd only produce zero if United 00:46:12.630 --> 00:46:16.300 was producing 192,000. 00:46:16.300 --> 00:46:18.980 Only at that point would they actually say, forget it, we're 00:46:18.980 --> 00:46:22.730 just going to produce zero. 00:46:22.730 --> 00:46:26.000 That's what the 192 point means. 00:46:26.000 --> 00:46:28.780 Only if they knew United was producing all that much would 00:46:28.780 --> 00:46:31.150 they just drop out of the market. 00:46:31.150 --> 00:46:33.440 So that's the 192 intersection. 00:46:33.440 --> 00:46:35.890 A backwards way to read the curves. 00:46:35.890 --> 00:46:39.480 But the bottom line, is essentially we can write these 00:46:39.480 --> 00:46:40.760 best response curves. 00:46:43.490 --> 00:46:47.520 They're basically the quantity I'm going to produce given the 00:46:47.520 --> 00:46:49.980 quantity the other firm produces. 00:46:49.980 --> 00:46:52.430 And the key thing is that these are 00:46:52.430 --> 00:46:55.030 symmetric in this example. 00:46:55.030 --> 00:46:59.180 Since the costs are the same and they both face the same 00:46:59.180 --> 00:47:03.540 market demand then these curves are symmetric. 00:47:07.380 --> 00:47:12.680 What that means is that these curves are having figured out 00:47:12.680 --> 00:47:16.020 one you can automatically draw the other. 00:47:16.020 --> 00:47:18.500 A trick for solving these problems is that if you have a 00:47:18.500 --> 00:47:21.490 symmetric Cournot equilibrium you don't need to calculate 00:47:21.490 --> 00:47:23.560 the math to find each firm's best response curve. 00:47:23.560 --> 00:47:26.080 Once you calculate one you know the other firm's just a 00:47:26.080 --> 00:47:27.570 complement of it. 00:47:27.570 --> 00:47:30.030 So having calculated American's best response curve 00:47:30.030 --> 00:47:32.590 we could have automatically drawn the United best response 00:47:32.590 --> 00:47:36.010 curve as a complement of that. 00:47:36.010 --> 00:47:39.500 The other key point is by drawing this diagram we can 00:47:39.500 --> 00:47:41.820 see the Cournot equilibrium. 00:47:41.820 --> 00:47:43.690 Remember Cournot equilibrium. 00:47:43.690 --> 00:47:47.930 Cournot equilibrium is where I'm happy with my quantity 00:47:47.930 --> 00:47:49.840 given what the other firm's doing. 00:47:49.840 --> 00:47:50.940 Given what the other firm's doing I can't 00:47:50.940 --> 00:47:52.280 make any more money. 00:47:52.280 --> 00:47:53.665 Once again, I don't care about market share, I just care 00:47:53.665 --> 00:47:54.860 about money. 00:47:54.860 --> 00:47:56.480 So given what the other firm's doing I can't 00:47:56.480 --> 00:47:57.480 make any more money. 00:47:57.480 --> 00:48:02.650 Well that happens at 64,000 each. 00:48:02.650 --> 00:48:05.920 Because when American is producing 64,000, United is 00:48:05.920 --> 00:48:07.540 happy to produce 64,000. 00:48:07.540 --> 00:48:09.590 That's their profit maximizing choice. 00:48:09.590 --> 00:48:11.530 If United is producing 64,000 American's 00:48:11.530 --> 00:48:12.860 happy to produce 64,000. 00:48:12.860 --> 00:48:15.110 That's their profit maximizing choice. 00:48:15.110 --> 00:48:18.500 So that point of each producing 64,000 we are in a 00:48:18.500 --> 00:48:20.630 Nash or Cournot equilibrium. 00:48:20.630 --> 00:48:23.780 Both firms are happy given what the other firm is doing. 00:48:23.780 --> 00:48:26.290 Both firms are profit maximizing given what the 00:48:26.290 --> 00:48:27.540 other firm is doing. 00:48:29.850 --> 00:48:33.630 Now basically, for example, another way to look at this is 00:48:33.630 --> 00:48:37.310 that you're only in equilibrium if you're on both 00:48:37.310 --> 00:48:39.390 firms' reaction curves. 00:48:39.390 --> 00:48:43.860 So, for example, American might say, look the 00:48:43.860 --> 00:48:47.060 equilibrium I like is where I do 96,000 00:48:47.060 --> 00:48:49.710 flights and you none. 00:48:49.710 --> 00:48:54.980 So the equilibrium I like is on the x-axis the point 96, 0, 00:48:54.980 --> 00:48:58.160 where I do 96,000 flights and you United do none. 00:48:58.160 --> 00:49:02.070 United says, however, no that's not optimal for me. 00:49:02.070 --> 00:49:03.480 Because if you're doing that, then you're 00:49:03.480 --> 00:49:07.000 charging a price of $243. 00:49:07.000 --> 00:49:08.170 So there's money to be made for me. 00:49:08.170 --> 00:49:10.570 I can come in and start stealing some of your flights. 00:49:10.570 --> 00:49:12.560 So that's not an equilibrium from my perspective. 00:49:12.560 --> 00:49:13.790 Might be an equilibrium from your perspective. 00:49:13.790 --> 00:49:15.820 You're delighted you're a monopolist. But not from my 00:49:15.820 --> 00:49:16.630 perspective. 00:49:16.630 --> 00:49:17.940 At that price I'll come in and start 00:49:17.940 --> 00:49:19.850 stealing some your business. 00:49:19.850 --> 00:49:20.670 And I'm going to start stealing 00:49:20.670 --> 00:49:21.190 some of your business. 00:49:21.190 --> 00:49:24.500 As I steal your business you are going to have to move up 00:49:24.500 --> 00:49:29.670 your best response curve because your residual demand 00:49:29.670 --> 00:49:30.890 is shrinking. 00:49:30.890 --> 00:49:32.950 And you'll only reach equilibrium when you're both 00:49:32.950 --> 00:49:33.830 happy with the outcome. 00:49:33.830 --> 00:49:35.695 If only one firm is happy with the outcome the other firm can 00:49:35.695 --> 00:49:38.200 always change its behavior, raise its price up or down or 00:49:38.200 --> 00:49:40.700 its quantity up or down to change the market share and 00:49:40.700 --> 00:49:41.820 change the outcome. 00:49:41.820 --> 00:49:44.330 So equilibrium will only be when you're at both firms best 00:49:44.330 --> 00:49:45.340 response curves. 00:49:45.340 --> 00:49:46.980 You'll only be at both firm's best response curves where 00:49:46.980 --> 00:49:49.270 they intersect. 00:49:49.270 --> 00:49:51.290 Let's stop there I'm going to come back next time. 00:49:53.820 --> 00:49:56.070 Jessica we should have the same handout next time. 00:49:56.070 --> 00:49:57.690 Let's make sure this figure is in the handout 00:49:57.690 --> 00:49:59.670 next time as well. 00:49:59.670 --> 00:50:01.670 And we'll come back and talk about this last figure and 00:50:01.670 --> 00:50:03.010 we'll do the math behind it as well.