1 00:00:00,040 --> 00:00:02,460 The following content is provided under a Creative 2 00:00:02,460 --> 00:00:03,870 Commons license. 3 00:00:03,870 --> 00:00:06,910 Your support will help MIT OpenCourseWare continue to 4 00:00:06,910 --> 00:00:10,560 offer high-quality educational resources for free. 5 00:00:10,560 --> 00:00:13,460 To make a donation or view additional materials from 6 00:00:13,460 --> 00:00:16,180 hundreds of MIT courses, visit mitopencourseware@ocw.mit.edu. 7 00:00:24,830 --> 00:00:25,920 PROFESSOR: Economics-- 8 00:00:25,920 --> 00:00:27,510 oligopoly. 9 00:00:27,510 --> 00:00:34,390 Which is basically trying to move towards the most 10 00:00:34,390 --> 00:00:39,150 realistic modeling of markets that we can. 11 00:00:39,150 --> 00:00:42,820 We've talked about two extreme versions of modeling markets. 12 00:00:42,820 --> 00:00:47,610 One is perfect competition, which is the extreme case of 13 00:00:47,610 --> 00:00:49,490 perfect entry and exit. 14 00:00:49,490 --> 00:00:50,920 Free entry and exit. 15 00:00:50,920 --> 00:00:52,630 Perfect consumer information. 16 00:00:52,630 --> 00:00:53,950 An idealized market. 17 00:00:53,950 --> 00:00:56,810 We know that doesn't really exist in practice anywhere. 18 00:00:56,810 --> 00:00:59,510 The second extreme was monopoly, which we do see in 19 00:00:59,510 --> 00:01:00,880 practice in some places. 20 00:01:00,880 --> 00:01:04,140 In particular, when there's natural monopolies. 21 00:01:04,140 --> 00:01:04,940 We do see that. 22 00:01:04,940 --> 00:01:07,520 But that's still doesn't describe most markets. 23 00:01:07,520 --> 00:01:10,970 Most markets are better described as oligopolies. 24 00:01:10,970 --> 00:01:14,160 These are markets where there's more than one market 25 00:01:14,160 --> 00:01:18,000 player, yet where each firm is large enough to actually 26 00:01:18,000 --> 00:01:20,430 affect the price. 27 00:01:20,430 --> 00:01:23,880 So an oligopoly market is where there'll be a small 28 00:01:23,880 --> 00:01:27,660 number of firms in the market with substantial barriers to 29 00:01:27,660 --> 00:01:31,190 entry from additional firms. An oligopoly market where 30 00:01:31,190 --> 00:01:34,300 there's a small number of firms with enough barriers to 31 00:01:34,300 --> 00:01:37,960 entry that additional firms don't enter. 32 00:01:37,960 --> 00:01:40,680 So the classic example of an oligopoly 33 00:01:40,680 --> 00:01:43,250 industry is the auto industry. 34 00:01:43,250 --> 00:01:47,000 Here's a market with a small number of dominant players. 35 00:01:47,000 --> 00:01:50,200 There's been some entry and exit over time, obviously, but 36 00:01:50,200 --> 00:01:51,870 it moves pretty slowly. 37 00:01:51,870 --> 00:01:53,850 By and large it's a market where there's 38 00:01:53,850 --> 00:01:55,780 very limited entry. 39 00:01:55,780 --> 00:02:00,110 And the question is, how do firms behave in this market? 40 00:02:00,110 --> 00:02:02,700 Obviously it's not like perfect competition where they 41 00:02:02,700 --> 00:02:05,750 can lazily take a price out of the market and just produce 42 00:02:05,750 --> 00:02:07,290 based on that price. 43 00:02:07,290 --> 00:02:09,199 But it's also not the same as monopoly where they can just 44 00:02:09,199 --> 00:02:10,639 get to set the price and not worry about what 45 00:02:10,639 --> 00:02:11,890 other people do. 46 00:02:11,890 --> 00:02:14,470 They're in this in-between situation where they have 47 00:02:14,470 --> 00:02:15,630 price setting power. 48 00:02:15,630 --> 00:02:18,220 They have some market power but in a context where they 49 00:02:18,220 --> 00:02:21,830 have to worry about competitors. 50 00:02:21,830 --> 00:02:25,510 And so in this context there are two different ways firms 51 00:02:25,510 --> 00:02:28,450 can behave. It's important to lay out to start. 52 00:02:28,450 --> 00:02:29,990 There's two different ways for firms to behave. They can 53 00:02:29,990 --> 00:02:34,130 behave cooperatively or non-cooperatively. 54 00:02:34,130 --> 00:02:36,510 If they behave cooperatively we say 55 00:02:36,510 --> 00:02:38,046 that they form a cartel. 56 00:02:40,620 --> 00:02:46,110 So our cartel is what happens when oligopolistic firms, when 57 00:02:46,110 --> 00:02:50,450 firms in an oligopolistic market behave cooperatively to 58 00:02:50,450 --> 00:02:51,220 determine the outcome. 59 00:02:51,220 --> 00:02:53,480 We call that a cartel. 60 00:02:53,480 --> 00:02:56,410 The classic example, of course, here being OPEC. 61 00:02:56,410 --> 00:02:59,680 The Organization of Petroleum Exporting Countries, which is 62 00:02:59,680 --> 00:03:04,830 a cartel that drives the price of oil. 63 00:03:04,830 --> 00:03:07,950 Those countries cooperate in how much oil they produce to 64 00:03:07,950 --> 00:03:09,880 move the price up or down according to 65 00:03:09,880 --> 00:03:12,930 what the group desires. 66 00:03:12,930 --> 00:03:18,170 And what cartels do is essentially turn oligopolies 67 00:03:18,170 --> 00:03:20,010 into monopolies. 68 00:03:20,010 --> 00:03:22,610 So what cartelization does, what a cooperative equilibrium 69 00:03:22,610 --> 00:03:25,380 does is essentially say, let's all get together and behave as 70 00:03:25,380 --> 00:03:26,905 if we're one big monopoly by cooperating. 71 00:03:30,130 --> 00:03:32,320 And therefore, if you cooperate you can get all the 72 00:03:32,320 --> 00:03:34,580 wonderful things monopolies get: huge market power, huge 73 00:03:34,580 --> 00:03:36,090 markets et cetera. 74 00:03:36,090 --> 00:03:38,760 But as we'll talk about next time, it turns out to be 75 00:03:38,760 --> 00:03:43,080 pretty hard to get a cooperative oligopoly. 76 00:03:43,080 --> 00:03:45,870 There's lots of reasons why it might fall apart. 77 00:03:45,870 --> 00:03:49,820 And that's why in most oligopolistic markets firms 78 00:03:49,820 --> 00:03:52,110 behave non cooperatively. 79 00:03:52,110 --> 00:03:55,160 In most oligopolistic markets firms are behaving 80 00:03:55,160 --> 00:03:56,490 non-cooperatively. 81 00:03:56,490 --> 00:04:00,360 They're competing with each other, not cooperating. 82 00:04:00,360 --> 00:04:03,900 And that's what we're going to spend today analyzing is the 83 00:04:03,900 --> 00:04:05,920 case of non-cooperative oligopolies. 84 00:04:17,420 --> 00:04:17,820 Yeah? 85 00:04:17,820 --> 00:04:19,070 AUDIENCE: [INAUDIBLE]? 86 00:04:21,660 --> 00:04:23,060 PROFESSOR: Depends on the context. 87 00:04:25,970 --> 00:04:28,470 In the US, and I'll talk about this, in the US there's 88 00:04:28,470 --> 00:04:31,860 anti-trust legislation which can make it illegal in many 89 00:04:31,860 --> 00:04:33,730 contexts to cooperate. 90 00:04:33,730 --> 00:04:37,600 Obviously OPEC is not subject to some world legislation. 91 00:04:37,600 --> 00:04:39,490 But even in the US there can be implicit cartelization and 92 00:04:39,490 --> 00:04:43,600 implicit cooperation, and we'll talk about that. 93 00:04:43,600 --> 00:04:45,020 It's a good question. 94 00:04:45,020 --> 00:04:46,050 So technically you're right. 95 00:04:46,050 --> 00:04:49,890 Technically it is illegal in the US in most contexts to 96 00:04:49,890 --> 00:04:52,470 form a cooperative, to form a cartel. 97 00:04:52,470 --> 00:04:55,780 Whether in practice those laws can be enforced is an 98 00:04:55,780 --> 00:04:57,040 interesting, legitimate question. 99 00:04:59,640 --> 00:05:02,050 So today we want to focus on the case of non-cooperative 100 00:05:02,050 --> 00:05:02,500 oligopolies. 101 00:05:02,500 --> 00:05:06,030 And to do so we're going to turn to a new tool. 102 00:05:06,030 --> 00:05:08,440 And one of the fundamental tools of economics in the last 103 00:05:08,440 --> 00:05:11,370 30 years which is game theory. 104 00:05:11,370 --> 00:05:15,050 So today we're going to talk about game theory. 105 00:05:15,050 --> 00:05:20,310 Game theory is a tool of economics that was not really 106 00:05:20,310 --> 00:05:25,640 used early in economics but has come to dominate 107 00:05:25,640 --> 00:05:30,210 theoretical economics over the past 30 or 40 years. 108 00:05:30,210 --> 00:05:33,820 And basically the way that game theory works is to think, 109 00:05:33,820 --> 00:05:38,790 literally, of oligopolistic firms as engaging in a game. 110 00:05:38,790 --> 00:05:42,420 So when you play, don't want to say play Monopoly, that's 111 00:05:42,420 --> 00:05:43,980 confusing terms. When you play Sorry! 112 00:05:43,980 --> 00:05:48,200 or whatever with someone, or play some online game with 113 00:05:48,200 --> 00:05:50,200 someone, you're competing to win. 114 00:05:50,200 --> 00:05:52,240 You're behaving non-cooperatively. 115 00:05:52,240 --> 00:05:54,250 You're competing to win. 116 00:05:54,250 --> 00:05:58,100 So basically what the insights of game theory are that all 117 00:05:58,100 --> 00:06:00,770 the tools we used strategically to make 118 00:06:00,770 --> 00:06:04,940 decisions in playing games can actually be used in modeling 119 00:06:04,940 --> 00:06:07,170 how firms compete non-cooperatively in 120 00:06:07,170 --> 00:06:08,420 oligopolistic market. 121 00:06:11,330 --> 00:06:17,010 The key insight is that each firm will develop a strategy. 122 00:06:17,010 --> 00:06:20,370 Just as when you're playing chess you have some strategy 123 00:06:20,370 --> 00:06:24,420 going in, firms develop a strategy. 124 00:06:24,420 --> 00:06:27,580 And that based on that strategy they will determine 125 00:06:27,580 --> 00:06:30,380 their behavior. 126 00:06:30,380 --> 00:06:36,470 And what is going to determine that behavior is going to be 127 00:06:36,470 --> 00:06:42,010 how firms' strategies combine to determine a market outcome. 128 00:06:42,010 --> 00:06:44,910 When firms come in with different strategies, or when 129 00:06:44,910 --> 00:06:46,560 a bunch of firms with strategies come in to compete 130 00:06:46,560 --> 00:06:50,355 with each other, what determines the market outcome. 131 00:06:50,355 --> 00:06:53,790 And what that's going to depend on is something we call 132 00:06:53,790 --> 00:06:55,305 an equilibrium concept. 133 00:06:59,940 --> 00:07:02,080 Which is how do we measure-- 134 00:07:02,080 --> 00:07:05,610 essentially the equilibrium concept is in game theory 135 00:07:05,610 --> 00:07:06,750 terms, think about how do we determine 136 00:07:06,750 --> 00:07:08,490 when the game's over? 137 00:07:08,490 --> 00:07:11,510 How do we determine when we've decided on the 138 00:07:11,510 --> 00:07:13,160 outcome of the market. 139 00:07:13,160 --> 00:07:14,260 What's the equilibrium concept? 140 00:07:14,260 --> 00:07:18,170 So when you're reading the rules of a new game the first 141 00:07:18,170 --> 00:07:20,230 thing you look for is how do you decide who wins. 142 00:07:20,230 --> 00:07:22,530 That's kind of like what the equilibrium concept is. 143 00:07:22,530 --> 00:07:26,900 It's what determines whether the game has ended. 144 00:07:26,900 --> 00:07:30,760 What determines whether you've reached equilibrium. 145 00:07:30,760 --> 00:07:33,170 Where you've reached a point where the market is stable and 146 00:07:33,170 --> 00:07:34,650 therefore the game has ended. 147 00:07:34,650 --> 00:07:36,390 Not ended in the sense the firm shut down, but ended in 148 00:07:36,390 --> 00:07:38,390 the sense that you know what everybody's doing. 149 00:07:38,390 --> 00:07:40,060 So it's not quite like winning or losing. 150 00:07:40,060 --> 00:07:41,870 It's more just like what determines when you're at the 151 00:07:41,870 --> 00:07:46,490 point where that market is at equilibrium. 152 00:07:46,490 --> 00:07:51,150 Now the most famous concept is due to John Nash, who many of 153 00:07:51,150 --> 00:07:53,900 you heard of from the movie and book A Beautiful Mind, and 154 00:07:53,900 --> 00:07:55,390 that's called the Nash Equilibrium. 155 00:08:01,210 --> 00:08:07,850 A Nash equilibrium is the point at which no firm wants 156 00:08:07,850 --> 00:08:11,030 to change its strategy given what the 157 00:08:11,030 --> 00:08:12,900 other firms are doing. 158 00:08:12,900 --> 00:08:13,860 I'm going to say that again. 159 00:08:13,860 --> 00:08:17,030 A Nash equilibrium is the point where no firm wants to 160 00:08:17,030 --> 00:08:21,940 change its strategy given what the other firms are doing. 161 00:08:21,940 --> 00:08:25,210 It's a little bit bizarre, but we'll work it out. 162 00:08:25,210 --> 00:08:31,230 In other words, more formally, the idea is that holding 163 00:08:31,230 --> 00:08:38,169 constant, given the strategies all your competitors use 164 00:08:38,169 --> 00:08:43,390 there's nothing that I can do to raise my profits further. 165 00:08:43,390 --> 00:08:46,640 Given the strategies all my competitors are playing, 166 00:08:46,640 --> 00:08:50,080 there's no strategy I can choose that will make me more 167 00:08:50,080 --> 00:08:52,110 profitable than the one I'm choosing. 168 00:08:52,110 --> 00:08:54,257 And likewise for every player in the market that will turn 169 00:08:54,257 --> 00:08:54,930 out to be true. 170 00:08:54,930 --> 00:08:56,860 So have players sitting around a game board, 171 00:08:56,860 --> 00:08:58,340 going around the circle. 172 00:08:58,340 --> 00:09:01,110 Each player says, given what I know each of the rest you are 173 00:09:01,110 --> 00:09:04,560 doing, I'm doing the best thing I can. 174 00:09:04,560 --> 00:09:06,780 And they go around the circle and everybody says, OK, I'm at 175 00:09:06,780 --> 00:09:08,050 that point. 176 00:09:08,050 --> 00:09:11,580 You've reached a stable Nash equilibrium. 177 00:09:11,580 --> 00:09:14,100 This was named, of course, for John Nash. 178 00:09:14,100 --> 00:09:15,530 You all know the story of John Nash. 179 00:09:15,530 --> 00:09:17,820 He was a famous, actually mathematician. 180 00:09:17,820 --> 00:09:21,650 We use his tools in economics, but he was a mathematician. 181 00:09:21,650 --> 00:09:23,770 Developed these incredible theories, and then developed 182 00:09:23,770 --> 00:09:25,920 schizophrenia, went crazy. 183 00:09:25,920 --> 00:09:29,010 But not before he developed some of the most important 184 00:09:29,010 --> 00:09:31,770 concepts in both mathematics and economics. 185 00:09:31,770 --> 00:09:34,460 The most important is the Nash equilibrium. 186 00:09:34,460 --> 00:09:39,170 Now the best illustration we use of the Nash equilibrium is 187 00:09:39,170 --> 00:09:41,680 an example that we refer to as the prisoner's dilemma. 188 00:09:48,380 --> 00:09:51,920 And many of you will be familiar with this from more 189 00:09:51,920 --> 00:09:53,330 popular reading you've done in economics. 190 00:09:53,330 --> 00:09:55,200 But let me just go through it because it's important to 191 00:09:55,200 --> 00:09:55,760 understand it. 192 00:09:55,760 --> 00:09:57,000 The prisoner's dilemma. 193 00:09:57,000 --> 00:10:01,960 The prisoner's dilemma the title comes from the old way 194 00:10:01,960 --> 00:10:03,370 they used to make police movies. 195 00:10:03,370 --> 00:10:06,670 Where the idea is you catch two guys at a crime. 196 00:10:06,670 --> 00:10:10,010 You can't put them away unless one of them fesses up. 197 00:10:10,010 --> 00:10:12,680 So what you do is you put them each a separate room. 198 00:10:12,680 --> 00:10:16,090 And you say to the one, your buddy's cracked. 199 00:10:16,090 --> 00:10:18,890 He's going to he's going to sell you down the river. 200 00:10:18,890 --> 00:10:22,610 You better, I'm using all my '50s analogies, he's going to 201 00:10:22,610 --> 00:10:25,010 put you away for good. 202 00:10:25,010 --> 00:10:28,530 But if you admit that he's guilty and he did the crime, 203 00:10:28,530 --> 00:10:30,980 we'll let you off with a light sentence. 204 00:10:30,980 --> 00:10:32,660 Then they go to the other room and say the same thing to the 205 00:10:32,660 --> 00:10:35,490 other guy hoping they'll both rat on each other and they'll 206 00:10:35,490 --> 00:10:38,580 both get a sentence. 207 00:10:38,580 --> 00:10:46,360 So basically the idea is, let's say that you walk into 208 00:10:46,360 --> 00:10:49,030 each room and you say to each person, look, we have enough 209 00:10:49,030 --> 00:10:51,330 evidence right here, and you show them, to send you each to 210 00:10:51,330 --> 00:10:53,850 prison for a year. 211 00:10:53,850 --> 00:10:55,400 We would have enough evidence to send you each to 212 00:10:55,400 --> 00:10:56,970 prison for a year. 213 00:10:56,970 --> 00:11:01,450 But we aren't sure about this other thing. 214 00:11:01,450 --> 00:11:03,980 If you'll admit that your friend did this other thing, 215 00:11:03,980 --> 00:11:06,834 then he'll go for five years and you'll go free. 216 00:11:06,834 --> 00:11:08,700 And then we go to the friend and say the same thing. 217 00:11:08,700 --> 00:11:10,360 If you'll admit that your friend did the other thing 218 00:11:10,360 --> 00:11:11,770 he'll go five years and you'll go free. 219 00:11:11,770 --> 00:11:17,070 But if they both admit then they both go for two years. 220 00:11:17,070 --> 00:11:18,980 So if they both admit, they both go for two years. 221 00:11:18,980 --> 00:11:21,360 Now the way to write this down, what we do here to 222 00:11:21,360 --> 00:11:25,410 explain this, is we write down what we call a payoff matrix. 223 00:11:25,410 --> 00:11:27,000 So write down a payoff matrix. 224 00:11:27,000 --> 00:11:31,640 So the idea is we have prisoner A here 225 00:11:31,640 --> 00:11:32,980 and prisoner B here. 226 00:11:36,910 --> 00:11:38,510 And they each have an option. 227 00:11:38,510 --> 00:11:43,300 They could remain silent or they can talk. 228 00:11:47,990 --> 00:11:49,240 Silent or talk. 229 00:11:52,270 --> 00:11:55,370 Now if they both remain silent, if they both say I 230 00:11:55,370 --> 00:11:57,780 would never rat out my friend, I'm happy to go to jail for a 231 00:11:57,780 --> 00:12:00,910 year rather than rat out my friend, then they each get one 232 00:12:00,910 --> 00:12:01,950 year in jail. 233 00:12:01,950 --> 00:12:04,890 a equals 1, b equals 1. 234 00:12:04,890 --> 00:12:11,020 However if prisoner A rats out his buddy and prisoner B 235 00:12:11,020 --> 00:12:15,785 chooses not to rat out his buddy, then A gets-- 236 00:12:18,345 --> 00:12:21,360 so I'm sorry, if prisoner A talks and 237 00:12:21,360 --> 00:12:23,210 prisoner B remains silent. 238 00:12:23,210 --> 00:12:26,230 Prisoner A talks, prisoner B remains silent, then A gets 239 00:12:26,230 --> 00:12:29,050 zero but B get five years in prison. 240 00:12:31,650 --> 00:12:35,520 On the other hand, if prisoner B rats out his friend, but a 241 00:12:35,520 --> 00:12:39,190 prisoner A is true and doesn't say anything, then prisoner A 242 00:12:39,190 --> 00:12:42,080 is going to get stuck with five years and prisoner B is 243 00:12:42,080 --> 00:12:44,140 going to get nothing. 244 00:12:44,140 --> 00:12:47,300 And if they both rat each other out then they 245 00:12:47,300 --> 00:12:48,550 both get two years. 246 00:12:55,430 --> 00:12:57,080 So people understand the payoff. 247 00:12:57,080 --> 00:12:59,150 Are there questions about the set-up here? 248 00:12:59,150 --> 00:13:01,150 This is complicated so got to make sure you 249 00:13:01,150 --> 00:13:03,220 understand the set-up. 250 00:13:03,220 --> 00:13:08,390 Now, could someone tell me, if A and B could truthfully 251 00:13:08,390 --> 00:13:11,975 cooperate, what would be the optimal cooperative strategy? 252 00:13:15,320 --> 00:13:16,203 Yeah. 253 00:13:16,203 --> 00:13:18,921 AUDIENCE: You both go for a year. 254 00:13:18,921 --> 00:13:20,950 PROFESSOR: Right, you'd both be silent. 255 00:13:20,950 --> 00:13:24,780 So the optimal cooperative strategy is clear, which is to 256 00:13:24,780 --> 00:13:26,370 both be silent. 257 00:13:26,370 --> 00:13:28,350 So if the cop said, you know what, we'll let you guys get 258 00:13:28,350 --> 00:13:30,510 together and discuss what you want to do first-- 259 00:13:30,510 --> 00:13:32,450 which the cops would never be stupid enough to do-- but if 260 00:13:32,450 --> 00:13:35,170 they did and the guys can trust each other, then that's 261 00:13:35,170 --> 00:13:36,420 the optimal cooperative strategy. 262 00:13:40,500 --> 00:13:44,150 What we call optimal in the language of game theory, we 263 00:13:44,150 --> 00:13:45,555 call that the dominant strategy. 264 00:13:52,000 --> 00:13:57,720 A dominant strategy is the best thing to do no matter 265 00:13:57,720 --> 00:14:02,780 what the other guy does is the dominant strategy. 266 00:14:02,780 --> 00:14:05,150 So the dominant cooperative equilibrium strategy is to 267 00:14:05,150 --> 00:14:07,570 both stay quiet. 268 00:14:07,570 --> 00:14:12,950 But what's the dominant, non-cooperative strategy? 269 00:14:12,950 --> 00:14:15,045 What is the dominant non-cooperative strategy? 270 00:14:18,520 --> 00:14:20,960 So the ways with dominant strategy, we run through. 271 00:14:20,960 --> 00:14:23,830 Take prisoner A, ask the following. 272 00:14:23,830 --> 00:14:26,830 The dominant strategy is, is there a strategy that makes 273 00:14:26,830 --> 00:14:31,300 him better off regardless of what B does. 274 00:14:31,300 --> 00:14:33,410 Is there a strategy that makes A better off regardless of 275 00:14:33,410 --> 00:14:34,020 what B does. 276 00:14:34,020 --> 00:14:34,790 Let's go through. 277 00:14:34,790 --> 00:14:42,760 If A remains silent, if B remains silent he gets a year. 278 00:14:42,760 --> 00:14:46,180 If B talks he gets five years. 279 00:14:46,180 --> 00:14:50,780 Now compare that to prisoner A strategy of talking. 280 00:14:50,780 --> 00:14:54,870 Well if he talks he's better off than if he doesn't talk, 281 00:14:54,870 --> 00:14:57,470 if B's remaining silent. 282 00:14:57,470 --> 00:14:59,430 If he talks he's better off than if he 283 00:14:59,430 --> 00:15:01,980 doesn't talk if B talks. 284 00:15:01,980 --> 00:15:07,010 That is regardless of what B does, he's better off talking. 285 00:15:07,010 --> 00:15:10,210 Regardless of what B chooses to do, his dominant strategy 286 00:15:10,210 --> 00:15:11,380 is to talk. 287 00:15:11,380 --> 00:15:14,740 Because if B is silent, he's better off if he talks. 288 00:15:14,740 --> 00:15:17,310 If B talks he's better off if he talks. 289 00:15:17,310 --> 00:15:22,670 So matter what B chooses to do, A is better off talking. 290 00:15:22,670 --> 00:15:23,930 What about B? 291 00:15:23,930 --> 00:15:26,680 Well B, by the same logic, is always better 292 00:15:26,680 --> 00:15:28,210 off talking as well. 293 00:15:28,210 --> 00:15:30,590 No matter what A chooses to do, B is 294 00:15:30,590 --> 00:15:33,060 better off if he talks. 295 00:15:33,060 --> 00:15:34,580 So where do we end up? 296 00:15:34,580 --> 00:15:37,760 What ends up as the Nash equilibrium? 297 00:15:37,760 --> 00:15:41,750 The Nash equilibrium is that both prisoners talk. 298 00:15:41,750 --> 00:15:46,040 The dominant strategy for both prisoners is to talk. 299 00:15:46,040 --> 00:15:48,770 And they both end up worse off than they could have if they 300 00:15:48,770 --> 00:15:51,260 could have cooperated. 301 00:15:51,260 --> 00:15:54,710 So the dominant non-cooperative strategy is to 302 00:15:54,710 --> 00:16:01,930 both talk, even though if they could get together they'd be 303 00:16:01,930 --> 00:16:03,700 better both not talking. 304 00:16:03,700 --> 00:16:05,410 And this is basically how game theory works. 305 00:16:05,410 --> 00:16:07,010 Game theory math gets incredibly hard. 306 00:16:07,010 --> 00:16:09,370 And if you're interested, 14.12 is one of our most 307 00:16:09,370 --> 00:16:11,690 popular undergraduate courses, game theory. 308 00:16:11,690 --> 00:16:14,110 It's a great course where you take this and go run with it 309 00:16:14,110 --> 00:16:15,330 for a whole semester. 310 00:16:15,330 --> 00:16:17,360 It gets very complicated mathematically. 311 00:16:17,360 --> 00:16:19,690 But the basic idea in game theory is pretty 312 00:16:19,690 --> 00:16:23,090 straightforward, which is just ask, are there dominant 313 00:16:23,090 --> 00:16:25,780 strategies that can be played by each player. 314 00:16:25,780 --> 00:16:28,360 If each player has a dominant strategy and those dominant 315 00:16:28,360 --> 00:16:32,480 strategies lead to a Nash equilibrium then you're done. 316 00:16:32,480 --> 00:16:34,125 Here we're in a Nash equilibrium. 317 00:16:34,125 --> 00:16:36,040 Why are we in a Nash Equilibrium? 318 00:16:36,040 --> 00:16:41,730 Because given that A has talked, B's strategy, which is 319 00:16:41,730 --> 00:16:44,090 talking is the optimal thing to do. 320 00:16:44,090 --> 00:16:47,590 Given that B has talked, A's strategy which is talking is 321 00:16:47,590 --> 00:16:48,850 the optimal thing to do. 322 00:16:48,850 --> 00:16:51,600 So given what the other person's doing, each person is 323 00:16:51,600 --> 00:16:52,650 doing the right thing. 324 00:16:52,650 --> 00:16:55,660 So you're in Nash equilibrium. 325 00:16:55,660 --> 00:16:58,570 Given that B has chosen to talk, A is talking. 326 00:16:58,570 --> 00:17:01,560 That's the profit maximizing thing to do. 327 00:17:01,560 --> 00:17:03,030 Given that A is talking, B is talking. 328 00:17:03,030 --> 00:17:04,890 That's the profit maximizing thing to do. 329 00:17:04,890 --> 00:17:07,629 So given the strategy the other player's chosen that's 330 00:17:07,629 --> 00:17:08,380 an equilibrium. 331 00:17:08,380 --> 00:17:08,879 Yeah. 332 00:17:08,879 --> 00:17:12,871 AUDIENCE: If they both talk and got 10 years would that be 333 00:17:12,871 --> 00:17:14,368 the Nash equilibrium. 334 00:17:14,368 --> 00:17:17,869 PROFESSOR: No if they both talk, the 10 years only 335 00:17:17,869 --> 00:17:19,339 happens if one talks and the other one doesn't. 336 00:17:19,339 --> 00:17:21,331 AUDIENCE: No, I mean like, [INAUDIBLE]. 337 00:17:21,331 --> 00:17:23,849 PROFESSOR: Oh, if they both got 10 years? 338 00:17:23,849 --> 00:17:24,849 So let's ask that. 339 00:17:24,849 --> 00:17:26,099 Let's change this. 340 00:17:29,150 --> 00:17:31,470 Now let's just rework it. 341 00:17:31,470 --> 00:17:32,760 So now what's A's choice? 342 00:17:32,760 --> 00:17:36,920 Well A if he talks and B's silent, 343 00:17:36,920 --> 00:17:38,560 then he's better talking. 344 00:17:38,560 --> 00:17:41,480 But if he talks and B talks, he's worse talking. 345 00:17:41,480 --> 00:17:45,190 So then what he does depends on what B does. 346 00:17:45,190 --> 00:17:47,340 What B does is going to depend on what A does. 347 00:17:47,340 --> 00:17:50,870 And we can't obviously see the Nash equilibrium here. 348 00:17:50,870 --> 00:17:52,610 Because there's no dominant strategy. 349 00:17:52,610 --> 00:17:55,120 What you do depends on what the other person does. 350 00:17:55,120 --> 00:17:56,350 So there's no dominant strategy. 351 00:17:56,350 --> 00:17:59,350 Dominant strategies only occur if there's something that you 352 00:17:59,350 --> 00:18:01,720 should do no matter what the other person does. 353 00:18:01,720 --> 00:18:04,800 So in this case were these are both 2, there is a dominant 354 00:18:04,800 --> 00:18:06,880 strategy, It's to talk. 355 00:18:06,880 --> 00:18:09,280 If those are both 10 there's no longer a dominant strategy 356 00:18:09,280 --> 00:18:13,360 so we can't quickly get the Nash equilibrium. 357 00:18:13,360 --> 00:18:16,250 It's a good question. 358 00:18:16,250 --> 00:18:19,690 Now this is not just a cute example that you can use for 359 00:18:19,690 --> 00:18:22,590 prisoners, but actually explains firm 360 00:18:22,590 --> 00:18:24,270 behavior in many contexts. 361 00:18:24,270 --> 00:18:27,920 So the best example I like to think of of this is to think 362 00:18:27,920 --> 00:18:30,130 about advertising. 363 00:18:30,130 --> 00:18:32,950 So imagine if Coke and Pepsi, and imagine a world where 364 00:18:32,950 --> 00:18:34,360 Pepsi was as popular as Coke. 365 00:18:34,360 --> 00:18:35,090 That should never happen. 366 00:18:35,090 --> 00:18:35,960 Coke's way better. 367 00:18:35,960 --> 00:18:37,880 But imagine that was that world. 368 00:18:37,880 --> 00:18:41,480 So imagine a world where if there's no advertising then 369 00:18:41,480 --> 00:18:44,760 basically Pepsi and Coke would split the market 50-50. 370 00:18:44,760 --> 00:18:46,000 Imagine that set up. 371 00:18:46,000 --> 00:18:48,770 So if Pepsi and Coke could agree not to advertise they'd 372 00:18:48,770 --> 00:18:52,660 split the market 50-50. 373 00:18:52,660 --> 00:18:55,050 However, it's going to turn out that while that may be the 374 00:18:55,050 --> 00:18:58,280 dominant cooperative outcome, that's not the dominant 375 00:18:58,280 --> 00:19:01,310 non-cooperative outcome because each firm is better 376 00:19:01,310 --> 00:19:05,615 off advertising if the other one doesn't, or regardless. 377 00:19:05,615 --> 00:19:07,820 So for example, imagine the following payoffs matrix. 378 00:19:07,820 --> 00:19:09,330 I'm just making this up. 379 00:19:09,330 --> 00:19:13,800 But here you have Pepsi and here you have Coke. 380 00:19:13,800 --> 00:19:15,780 And imagine the payoff matrix. 381 00:19:15,780 --> 00:19:26,650 And the payoff matrix is if they don't advertise, so Pepsi 382 00:19:26,650 --> 00:19:29,435 can choose not to advertise, or it can advertise. 383 00:19:33,220 --> 00:19:36,910 So if they both don't advertise Pepsi gets 8 and 384 00:19:36,910 --> 00:19:37,510 Coke gets 8. 385 00:19:37,510 --> 00:19:38,110 I don't know what 8 is. 386 00:19:38,110 --> 00:19:39,230 8 is billion dollars. 387 00:19:39,230 --> 00:19:40,950 I'm just making up numbers here, doesn't matter. 388 00:19:40,950 --> 00:19:44,450 So $8 billion each. 389 00:19:44,450 --> 00:19:49,840 If they both do advertise then they still end up splitting 390 00:19:49,840 --> 00:19:50,320 the market. 391 00:19:50,320 --> 00:19:52,880 Because basically they're just as good as each other. 392 00:19:52,880 --> 00:19:54,510 So they both spend all the money advertising and just 393 00:19:54,510 --> 00:19:57,250 back up where they would have started, except they've wasted 394 00:19:57,250 --> 00:19:59,000 all this money in advertising. 395 00:19:59,000 --> 00:20:02,170 So if they both advertise they each earn $3 billion instead 396 00:20:02,170 --> 00:20:03,320 of $8 billion. 397 00:20:03,320 --> 00:20:04,410 That is, they each split the market. 398 00:20:04,410 --> 00:20:05,540 They end up back where they would have started but they 399 00:20:05,540 --> 00:20:08,760 pissed away a bunch of money advertising along the way. 400 00:20:08,760 --> 00:20:12,120 However if Coke advertised and Pepsi doesn't. 401 00:20:14,990 --> 00:20:16,696 Then almost everybody sees Coke, Coke, Coke everywhere 402 00:20:16,696 --> 00:20:17,440 and is like, Pepsi? 403 00:20:17,440 --> 00:20:19,320 Never heard of that. 404 00:20:19,320 --> 00:20:24,300 Coke makes $13 billion and Pepsi loses $2 billion. 405 00:20:24,300 --> 00:20:27,250 And likewise if Coke doesn't advertise but Pepsi does, 406 00:20:27,250 --> 00:20:28,230 people are like, I've never heard of Coke. 407 00:20:28,230 --> 00:20:30,270 I'm going to drink Pepsi. 408 00:20:30,270 --> 00:20:33,785 So Pepsi makes $13 billion and Coke makes minus $2 billion. 409 00:20:33,785 --> 00:20:36,550 Once again I just made numbers here so it would work, but 410 00:20:36,550 --> 00:20:40,360 these aren't real world examples. 411 00:20:40,360 --> 00:20:43,080 So once again we can see there is a dominant cooperative 412 00:20:43,080 --> 00:20:44,930 strategy, which is they both should 413 00:20:44,930 --> 00:20:48,150 agree let's not advertise. 414 00:20:48,150 --> 00:20:53,170 But if they can cooperate, then in fact what's the Nash 415 00:20:53,170 --> 00:20:53,700 equilibrium? 416 00:20:53,700 --> 00:20:54,840 Let's work it through. 417 00:20:54,840 --> 00:20:55,730 And there's no shortcuts here. 418 00:20:55,730 --> 00:20:56,670 You've just got to work this through. 419 00:20:56,670 --> 00:20:57,860 Let's look for Pepsi. 420 00:20:57,860 --> 00:21:01,450 Well Pepsi says if Coke doesn't advertise I'm better 421 00:21:01,450 --> 00:21:01,610 off advertising. 422 00:21:01,610 --> 00:21:02,860 If Coke does advertise, I'm better off advertising. 423 00:21:06,520 --> 00:21:09,240 So my dominant strategy is to advertise. 424 00:21:09,240 --> 00:21:14,980 Coke says, well gee, if Pepsi doesn't advertise I'm better 425 00:21:14,980 --> 00:21:15,530 off advertising. 426 00:21:15,530 --> 00:21:17,000 I make $13 billion instead of $8 billion. 427 00:21:17,000 --> 00:21:19,840 If Pepsi does advertise I make $3 billion instead of negative 428 00:21:19,840 --> 00:21:20,000 $2 billion. 429 00:21:20,000 --> 00:21:21,440 So I'm better off advertising too. 430 00:21:21,440 --> 00:21:24,060 So my dominant strategy is to advertise. 431 00:21:24,060 --> 00:21:26,960 So for both firms the dominant non-cooperative 432 00:21:26,960 --> 00:21:28,220 strategy is to advertise. 433 00:21:28,220 --> 00:21:32,110 So they both advertise and you end up in this equilibrium. 434 00:21:32,110 --> 00:21:36,380 It's an example of how a non-cooperative equilibrium 435 00:21:36,380 --> 00:21:39,680 can lead to what we call a race to the bottom. 436 00:21:39,680 --> 00:21:41,520 You can think of it as a race to the bottom. 437 00:21:41,520 --> 00:21:43,120 In other words, if they could cooperate they could just be 438 00:21:43,120 --> 00:21:43,550 better off. 439 00:21:43,550 --> 00:21:46,460 But because they can't trust the other, there's this race 440 00:21:46,460 --> 00:21:50,410 to the bottom where they both end up worse off. 441 00:21:50,410 --> 00:21:52,730 This is pretty striking. 442 00:21:52,730 --> 00:21:55,670 I thought they brought this out well in A Beautiful Mind, 443 00:21:55,670 --> 00:21:58,550 both the movie and the book, which is that all we've 444 00:21:58,550 --> 00:22:01,180 learned about economics so far is that 445 00:22:01,180 --> 00:22:03,520 competition is good, right? 446 00:22:03,520 --> 00:22:04,940 Competition is beneficial. 447 00:22:04,940 --> 00:22:07,190 Well here's a case, where in fact, at least in the firm's 448 00:22:07,190 --> 00:22:09,750 perspective, competition is bad. 449 00:22:09,750 --> 00:22:13,670 If they could just get together and cooperate they 450 00:22:13,670 --> 00:22:16,570 could make more money. 451 00:22:16,570 --> 00:22:21,470 Now, in fact, this example is not so far-fetched. 452 00:22:21,470 --> 00:22:22,810 I don't know when it started but it 453 00:22:22,810 --> 00:22:23,930 was during your lifetimes. 454 00:22:23,930 --> 00:22:30,460 When you were young, hard liquors, scotch, bourbon, 455 00:22:30,460 --> 00:22:34,290 whisky, et cetera, did not advertise on television. 456 00:22:34,290 --> 00:22:38,090 You never saw a Johnny Walker ad or anything on television 457 00:22:38,090 --> 00:22:39,690 until, I don't know when it changed maybe five 458 00:22:39,690 --> 00:22:41,250 or six years ago. 459 00:22:41,250 --> 00:22:42,150 Maybe 10 years ago, I don't know. 460 00:22:42,150 --> 00:22:43,860 But certainly in your lifetimes. 461 00:22:43,860 --> 00:22:45,250 That was not by government regulation. 462 00:22:45,250 --> 00:22:46,370 Many people thought there was a government 463 00:22:46,370 --> 00:22:47,210 regulation, they couldn't. 464 00:22:47,210 --> 00:22:48,060 That was not. 465 00:22:48,060 --> 00:22:50,470 That was a cooperative equilibrium where the makers 466 00:22:50,470 --> 00:22:53,500 of hard liquors got together and agreed not to advertise on 467 00:22:53,500 --> 00:22:55,800 TV. And they said it was in the "public interest" yada 468 00:22:55,800 --> 00:22:58,370 yada yada, but that wasn't. 469 00:22:58,370 --> 00:23:01,040 It was just they recognized the benefits of cooperating 470 00:23:01,040 --> 00:23:02,720 and not wasting money advertising on TV and 471 00:23:02,720 --> 00:23:04,020 competing with each other. 472 00:23:04,020 --> 00:23:06,990 Well that broke down some number of years ago. 473 00:23:06,990 --> 00:23:09,706 And now you see whiskey ads and scotch ads and other 474 00:23:09,706 --> 00:23:10,820 things on television. 475 00:23:10,820 --> 00:23:14,220 And they've moved to this non-cooperative equilibrium 476 00:23:14,220 --> 00:23:15,865 where they're all losing money by having this advertising. 477 00:23:21,080 --> 00:23:23,410 So that's in advertising. 478 00:23:23,410 --> 00:23:26,660 For me, once again, this is a hard thing, what intuition 479 00:23:26,660 --> 00:23:27,540 works for you. 480 00:23:27,540 --> 00:23:30,320 For me the intuition works best maybe from my scars from 481 00:23:30,320 --> 00:23:33,890 my dating life is thinking about personal decisions. 482 00:23:33,890 --> 00:23:36,970 So imagine that there's some girl named Allison. 483 00:23:36,970 --> 00:23:39,600 And Allison has a potential problem with her boyfriend. 484 00:23:39,600 --> 00:23:42,970 They've had a fight and now she's deciding whether or not 485 00:23:42,970 --> 00:23:46,010 to make up or break up. 486 00:23:46,010 --> 00:23:48,720 Now we can think of this just like Coke and Pepsi. 487 00:23:48,720 --> 00:23:51,070 Allison is going to be thinking, well gee, if he 488 00:23:51,070 --> 00:23:53,790 wants to make up with me and I want to make up with him then 489 00:23:53,790 --> 00:23:55,230 we're both better off. 490 00:23:55,230 --> 00:23:57,470 But if I want to make up with him and he doesn't want to 491 00:23:57,470 --> 00:24:00,920 make up with me, that makes me look like a total idiot. 492 00:24:00,920 --> 00:24:05,210 Whereas if I break up with him preemptively, yes it would be 493 00:24:05,210 --> 00:24:08,040 sad if he wanted to stay with me, but at least if he wanted 494 00:24:08,040 --> 00:24:10,150 to break up with me I look better. 495 00:24:10,150 --> 00:24:12,880 So she preemptively breaks up with him. 496 00:24:12,880 --> 00:24:16,550 John, her boyfriend, thinking the same thing, behaves in 497 00:24:16,550 --> 00:24:17,970 exactly the same way. 498 00:24:17,970 --> 00:24:20,940 So it could be that even though they both would be 499 00:24:20,940 --> 00:24:23,890 better off if they just said, look the honest truth is, 500 00:24:23,890 --> 00:24:26,470 we're both wrong, let's make up and we'll both be happy. 501 00:24:26,470 --> 00:24:28,590 Because they're so afraid of being the one being dumped, 502 00:24:28,590 --> 00:24:30,740 they end up breaking up. 503 00:24:30,740 --> 00:24:33,560 Now we all know of examples like this from life, where 504 00:24:33,560 --> 00:24:36,720 people stupidly if they could have just cooperated had a 505 00:24:36,720 --> 00:24:38,830 better outcome because they're so afraid of being left with 506 00:24:38,830 --> 00:24:40,740 the short end of the stick, because they don't cooperate 507 00:24:40,740 --> 00:24:42,780 you end up with the worst outcome for both. 508 00:24:42,780 --> 00:24:44,310 That's an example of a non-cooperative 509 00:24:44,310 --> 00:24:48,090 equilibrium in real life. 510 00:24:48,090 --> 00:24:53,610 Now in real life there is one aspect of oligopolistic 511 00:24:53,610 --> 00:24:58,240 non-cooperative equilibria that allow them to be 512 00:24:58,240 --> 00:24:59,000 enforced, however. 513 00:24:59,000 --> 00:25:01,790 That allow you to overcome the prisoner's dilemma. 514 00:25:01,790 --> 00:25:03,470 There's one thing that allows you to overcome the prisoner's 515 00:25:03,470 --> 00:25:06,225 dilemma and that's repeated games. 516 00:25:14,550 --> 00:25:16,890 Repeated games can help you overcome 517 00:25:16,890 --> 00:25:18,140 the prisoner's dilemma. 518 00:25:20,920 --> 00:25:25,420 Now let's take the Coke and Pepsi example and let's 519 00:25:25,420 --> 00:25:28,830 imagine that they're making the advertising 520 00:25:28,830 --> 00:25:29,840 decision every period. 521 00:25:29,840 --> 00:25:30,590 Every period they have to make an 522 00:25:30,590 --> 00:25:32,730 independent advertising decision. 523 00:25:32,730 --> 00:25:36,240 They can advertise or not advertise every period. 524 00:25:36,240 --> 00:25:39,170 And imagine Coke says to Pepsi, I've got the following 525 00:25:39,170 --> 00:25:41,060 deal for you. 526 00:25:41,060 --> 00:25:47,210 I commit to not advertise as long as you don't, but the 527 00:25:47,210 --> 00:25:51,540 minute you advertise I'm going to advertise forever. 528 00:25:51,540 --> 00:25:54,310 So as long as you don't advertise I won't. 529 00:25:54,310 --> 00:25:56,900 But if you ever run an ad, the bet's off and I'm never going 530 00:25:56,900 --> 00:25:57,720 to cooperate with you. 531 00:25:57,720 --> 00:26:00,400 I'm going to advertise forever. 532 00:26:00,400 --> 00:26:04,310 Let's think about Pepsi's choice in period one if Coke 533 00:26:04,310 --> 00:26:05,190 presents them with this deal. 534 00:26:05,190 --> 00:26:06,930 Let's think about Pepsi's choice if Coke presents them 535 00:26:06,930 --> 00:26:09,180 with this deal. 536 00:26:09,180 --> 00:26:12,450 Well one thing is they could say, ha ha, great Coke, good 537 00:26:12,450 --> 00:26:13,210 job trusting me. 538 00:26:13,210 --> 00:26:15,560 I'm going to screw you in advertising period one. 539 00:26:15,560 --> 00:26:18,130 So Pepsi could say, great, Coke's laid down arms in 540 00:26:18,130 --> 00:26:19,170 period one. 541 00:26:19,170 --> 00:26:20,460 I'm going to go and advertise. 542 00:26:20,460 --> 00:26:22,250 I'll make $13 billion in period one because Coke's 543 00:26:22,250 --> 00:26:23,210 wimped out. 544 00:26:23,210 --> 00:26:26,160 And then I'll make $3 billion forever after, because forever 545 00:26:26,160 --> 00:26:27,400 after we're both going to advertise. 546 00:26:27,400 --> 00:26:30,400 But at least I' beat them up that first period. 547 00:26:30,400 --> 00:26:33,570 However, if Pepsi says, wait a second, if Coke's really 548 00:26:33,570 --> 00:26:36,930 right, honest, then I can get an equilibrium where we make 549 00:26:36,930 --> 00:26:38,780 $8 billion forever. 550 00:26:38,780 --> 00:26:40,790 And certainly $8 billion forever a better deal than $13 551 00:26:40,790 --> 00:26:43,330 billion one year and $3 billion forever. 552 00:26:43,330 --> 00:26:47,560 So in fact if Coke's willing to live up to that promise 553 00:26:47,560 --> 00:26:49,000 then that is a good deal. 554 00:26:49,000 --> 00:26:51,360 And actually we can turn this non-cooperative equilibrium 555 00:26:51,360 --> 00:26:53,770 into a cooperative equilibrium through the enforcement of a 556 00:26:53,770 --> 00:26:55,570 repeated game. 557 00:26:55,570 --> 00:26:57,650 Through the fact that this game gets played over and over 558 00:26:57,650 --> 00:27:05,940 and over again you can enforce a cooperative equilibrium. 559 00:27:05,940 --> 00:27:07,970 We can come back to relationships again. 560 00:27:07,970 --> 00:27:10,910 If you're in a committed relationship and you know that 561 00:27:10,910 --> 00:27:13,020 if I say it's your fault over and over again, eventually 562 00:27:13,020 --> 00:27:16,230 person's going to leave. Then people say gee, I'm willing to 563 00:27:16,230 --> 00:27:18,460 take some of the blame and not always say it's your fault and 564 00:27:18,460 --> 00:27:19,620 we have a fight. 565 00:27:19,620 --> 00:27:21,230 Because I know that if I always say it's your fault 566 00:27:21,230 --> 00:27:22,740 ultimately that will break the relationship up and that makes 567 00:27:22,740 --> 00:27:26,180 me worse off then admitting it was my fault some of the time. 568 00:27:26,180 --> 00:27:27,470 It's the same logic. 569 00:27:27,470 --> 00:27:27,860 Yeah. 570 00:27:27,860 --> 00:27:30,480 AUDIENCE: Is the point of the game to make more than the 571 00:27:30,480 --> 00:27:31,510 other guy or to make as much as possible? 572 00:27:31,510 --> 00:27:34,580 PROFESSOR: Make as much as possible. 573 00:27:34,580 --> 00:27:35,530 That's a good point. 574 00:27:35,530 --> 00:27:39,570 I presume that the point is to make as much as possible. 575 00:27:39,570 --> 00:27:41,850 I'm ruling out cut off your nose to spite your face 576 00:27:41,850 --> 00:27:42,920 equilibria. 577 00:27:42,920 --> 00:27:45,230 So in other words, I'm assuming the goals is to 578 00:27:45,230 --> 00:27:48,050 maximize profits not relevant mark position. 579 00:27:48,050 --> 00:27:48,830 That's a good point. 580 00:27:48,830 --> 00:27:49,920 I should have made that assumption clear. 581 00:27:49,920 --> 00:27:54,000 It's the assumption we're always making whatever we 582 00:27:54,000 --> 00:27:58,270 confirm behavior is assuming it's profit maximization. 583 00:27:58,270 --> 00:28:03,280 So repeated games can enforce a cooperative equilibria, 584 00:28:03,280 --> 00:28:04,080 essentially. 585 00:28:04,080 --> 00:28:06,550 Even in a non-cooperative set up. 586 00:28:06,550 --> 00:28:10,570 But it turns out this only works if the 587 00:28:10,570 --> 00:28:11,820 game goes on forever. 588 00:28:14,060 --> 00:28:16,440 This only works if the game is going to go on forever. 589 00:28:16,440 --> 00:28:22,450 So, for example, imagine that Pepsi knows that in 10 years 590 00:28:22,450 --> 00:28:24,380 the US government is going to ban the advertisement of 591 00:28:24,380 --> 00:28:26,080 sugared sodas. 592 00:28:26,080 --> 00:28:27,640 The US government is going to finally say, look, people are 593 00:28:27,640 --> 00:28:30,040 too obese, no more advertising sugary sodas. 594 00:28:30,040 --> 00:28:31,710 Pepsi knows this. 595 00:28:31,710 --> 00:28:33,590 In 10 years that's going to happen. 596 00:28:33,590 --> 00:28:36,270 Well Pepsi's thinking, gee, that means in 597 00:28:36,270 --> 00:28:39,790 year 10 I should advertise. 598 00:28:39,790 --> 00:28:41,580 In that last year I should advertise because Coke can't 599 00:28:41,580 --> 00:28:43,160 punish me the next year because no one can advertise 600 00:28:43,160 --> 00:28:44,340 the next year. 601 00:28:44,340 --> 00:28:46,410 So I know starting after 10 years we're both in this 602 00:28:46,410 --> 00:28:47,960 equilibrium because the government's 603 00:28:47,960 --> 00:28:48,900 going to enforce it. 604 00:28:48,900 --> 00:28:52,070 So in ninth year, right beforehand, right before that 605 00:28:52,070 --> 00:28:56,080 government ban I should advertise and Coke can't get 606 00:28:56,080 --> 00:28:57,480 me the next period because they don't have the 607 00:28:57,480 --> 00:28:59,140 tool to punish me. 608 00:28:59,140 --> 00:29:00,980 Well Coke, of course, knows Pepsi is going 609 00:29:00,980 --> 00:29:02,680 to behave that way. 610 00:29:02,680 --> 00:29:04,430 So Coke says, wait a second, if Pepsi's going to behave 611 00:29:04,430 --> 00:29:06,680 that way then I better advertise in the ninth period 612 00:29:06,680 --> 00:29:09,540 too or I'm going to get hit with a minus $2 billion. 613 00:29:09,540 --> 00:29:12,480 So I'm going to advertise in the ninth period too. 614 00:29:12,480 --> 00:29:14,305 Well Pepsi says, look, if Coke's going to advertise in 615 00:29:14,305 --> 00:29:15,600 the ninth period for sure, I may as well advertise in the 616 00:29:15,600 --> 00:29:18,170 eight period because Coke's going to advertise in the 617 00:29:18,170 --> 00:29:18,980 ninth period for sure. 618 00:29:18,980 --> 00:29:20,910 And by the same logic you can work it back that they'll both 619 00:29:20,910 --> 00:29:22,220 advertise right away and you'll end up with a 620 00:29:22,220 --> 00:29:24,300 non-cooperative equilibrium. 621 00:29:24,300 --> 00:29:29,290 That is a repeated game that does not enforce the 622 00:29:29,290 --> 00:29:30,700 cooperative equilibrium. 623 00:29:30,700 --> 00:29:34,260 Because by working that logic backwards if it ends in some 624 00:29:34,260 --> 00:29:37,230 realistic time frame, then you better off just breaking it 625 00:29:37,230 --> 00:29:39,060 now rather waiting for that period where 626 00:29:39,060 --> 00:29:40,670 you're the one who loses. 627 00:29:40,670 --> 00:29:41,080 Yeah. 628 00:29:41,080 --> 00:29:44,050 AUDIENCE: [INAUDIBLE] 629 00:29:44,050 --> 00:29:46,030 what if Pepsi [INAUDIBLE]? 630 00:29:46,030 --> 00:29:47,290 PROFESSOR: Exactly. 631 00:29:47,290 --> 00:29:50,400 If they don't then you could imagine that if Pepsi knows 632 00:29:50,400 --> 00:29:53,583 this and Coke doesn't, then Pepsi's optimal strategy will 633 00:29:53,583 --> 00:29:55,810 be to cooperate to the next to last period then go ahead and 634 00:29:55,810 --> 00:29:57,480 screw Coke and then Coke will lose. 635 00:29:57,480 --> 00:30:01,020 But presuming symmetric information, repeated games 636 00:30:01,020 --> 00:30:04,890 cannot enforce these equilibria if they end. 637 00:30:04,890 --> 00:30:10,930 So this is just an incredibly quick introduction to the fun 638 00:30:10,930 --> 00:30:13,530 that is game theory. 639 00:30:13,530 --> 00:30:16,510 We're going to go on now and do more rigorous versions of 640 00:30:16,510 --> 00:30:17,460 these models. 641 00:30:17,460 --> 00:30:20,125 But this is just to get you excited about the tools you 642 00:30:20,125 --> 00:30:22,270 can do with game theory with fun examples. 643 00:30:22,270 --> 00:30:23,880 Game theory is about taking these fun examples and 644 00:30:23,880 --> 00:30:25,190 thinking a lot harder about a lot. 645 00:30:25,190 --> 00:30:28,320 What if there's asymmetric information? 646 00:30:28,320 --> 00:30:31,905 What if the game ends long enough in the future that 647 00:30:31,905 --> 00:30:33,000 you're willing to be patient? 648 00:30:33,000 --> 00:30:35,270 How far off in the future does the game have to end to still 649 00:30:35,270 --> 00:30:36,700 enforce the cooperate equilibrium? 650 00:30:36,700 --> 00:30:38,270 What if there are three players? 651 00:30:38,270 --> 00:30:40,680 What if players move in different orders? 652 00:30:40,680 --> 00:30:42,440 What if one player goes first, the second player responds to 653 00:30:42,440 --> 00:30:44,670 that, is it different than if they go simultaneously? 654 00:30:44,670 --> 00:30:46,690 These are all really interesting issues that are 655 00:30:46,690 --> 00:30:49,060 very relevant to the real world firm behavior that you 656 00:30:49,060 --> 00:30:50,090 learn about game theory. 657 00:30:50,090 --> 00:30:53,890 So this is just to whet your appetite for that. 658 00:30:53,890 --> 00:30:57,190 Having done that we're going to now turn, leave aside these 659 00:30:57,190 --> 00:30:59,430 more interesting dynamic issues and focus on a specific 660 00:30:59,430 --> 00:31:04,120 example of a non-cooperative oligopoly. 661 00:31:04,120 --> 00:31:07,400 Because, once again, this is all fun intuitively, but we 662 00:31:07,400 --> 00:31:09,620 want you to be able to work through a problem. 663 00:31:09,620 --> 00:31:10,902 And the way to work that through is we're going to have 664 00:31:10,902 --> 00:31:14,290 to move to a specific, simplified example. 665 00:31:14,290 --> 00:31:16,280 And the example we're going to focus on is 666 00:31:16,280 --> 00:31:18,070 called the Cournot model. 667 00:31:21,490 --> 00:31:27,695 The Cournot model of non-cooperative oligopoly. 668 00:31:30,900 --> 00:31:34,340 The way we're going to do this here, is we're going to return 669 00:31:34,340 --> 00:31:38,320 to the example we had with the prisoner's dilemma. 670 00:31:38,320 --> 00:31:41,350 But instead of just facing two choices, talk or not talk, 671 00:31:41,350 --> 00:31:43,770 we're going to talk about firms facing a whole continuum 672 00:31:43,770 --> 00:31:44,750 of choices. 673 00:31:44,750 --> 00:31:49,040 Firms choosing how much they produce in a non-cooperative 674 00:31:49,040 --> 00:31:51,550 equilibria situation. 675 00:31:51,550 --> 00:31:53,420 So, for example, let's take the example 676 00:31:53,420 --> 00:31:54,500 they use in the book. 677 00:31:54,500 --> 00:31:58,160 Let's imagine there's two airlines that fly between New 678 00:31:58,160 --> 00:32:00,590 York and Chicago, American and United. 679 00:32:00,590 --> 00:32:02,230 And let's imagine for simplicity those are the only 680 00:32:02,230 --> 00:32:02,830 two airlines. 681 00:32:02,830 --> 00:32:04,680 Because of the hub and spoke system we talked about last 682 00:32:04,680 --> 00:32:09,270 time, let's say all the gates in Chicago that are available 683 00:32:09,270 --> 00:32:11,130 to come from New York are taken by two airlines-- 684 00:32:11,130 --> 00:32:12,260 United and American. 685 00:32:12,260 --> 00:32:14,170 Those are your only two options 686 00:32:14,170 --> 00:32:17,440 flying New York to Chicago. 687 00:32:17,440 --> 00:32:20,920 And the question we want to ask is, get in that world, how 688 00:32:20,920 --> 00:32:23,890 do United and American decide how many flights to run and 689 00:32:23,890 --> 00:32:26,690 what price to charge? 690 00:32:26,690 --> 00:32:27,980 If they're monopolies we'd know. 691 00:32:27,980 --> 00:32:29,195 If it was a perfect competition we'd know, but how 692 00:32:29,195 --> 00:32:30,445 do they decide this all oligopolistic. 693 00:32:35,650 --> 00:32:38,630 The way we figure this out is by looking for the Nash 694 00:32:38,630 --> 00:32:40,520 equilibrium in this case, which we also call Cournot 695 00:32:40,520 --> 00:32:43,240 equilibrium. 696 00:32:43,240 --> 00:32:53,770 Which is basically the quantity is chosen by each 697 00:32:53,770 --> 00:33:02,490 firm such that holding all other 698 00:33:02,490 --> 00:33:03,740 firms' quantities constant. 699 00:33:11,670 --> 00:33:15,320 So each firm chooses quantity such that holding all other 700 00:33:15,320 --> 00:33:19,545 firm's quantities constant they are maximizing profits. 701 00:33:24,750 --> 00:33:28,270 So I choose a quantity such that holding all the other 702 00:33:28,270 --> 00:33:31,470 firm's quantities constant I'm choosing a 703 00:33:31,470 --> 00:33:32,940 profit-maximizing quantity. 704 00:33:36,740 --> 00:33:42,360 And if each firm can choose a quantity that makes the market 705 00:33:42,360 --> 00:33:45,510 function where this is met, then you're in Cournot 706 00:33:45,510 --> 00:33:47,450 equilibrium. 707 00:33:47,450 --> 00:33:49,310 You're in Cournot equilibrium when each firm has 708 00:33:49,310 --> 00:33:50,780 decided, I'm happy. 709 00:33:50,780 --> 00:33:52,290 It's the same as the Nash concept. 710 00:33:52,290 --> 00:33:56,480 I'm happy with what I'm producing given what everybody 711 00:33:56,480 --> 00:33:57,410 else is producing. 712 00:33:57,410 --> 00:34:00,030 If everybody feels that way then you're in a Nash 713 00:34:00,030 --> 00:34:03,220 equilibrium or a Cournot equilibrium. 714 00:34:03,220 --> 00:34:06,460 So to see this, this is not immediately intuitive. 715 00:34:06,460 --> 00:34:07,900 Let me just talk you through the steps of how 716 00:34:07,900 --> 00:34:09,860 you'd solve for this. 717 00:34:09,860 --> 00:34:11,789 How do you actually solve for a Cournot equilibrium? 718 00:34:16,370 --> 00:34:18,560 So basically what are the steps to solving? 719 00:34:18,560 --> 00:34:24,400 Step one for solving a Cournot equilibrium is to create each 720 00:34:24,400 --> 00:34:25,900 firm's residual demand. 721 00:34:25,900 --> 00:34:28,800 So compute residual demand. 722 00:34:28,800 --> 00:34:32,909 We talked about residual demand curves earlier. 723 00:34:32,909 --> 00:34:36,940 Which is, that's the demand for my firm given the quantity 724 00:34:36,940 --> 00:34:39,300 absorbed by other firms in the market. 725 00:34:39,300 --> 00:34:41,159 In this case it's quantities absorbed by the one other firm 726 00:34:41,159 --> 00:34:42,699 in the market, but in general you do this 727 00:34:42,699 --> 00:34:44,050 with multiple players. 728 00:34:44,050 --> 00:34:45,689 So first you calculate residual demand. 729 00:34:49,909 --> 00:34:58,660 Then having computed your residual demand you develop a 730 00:34:58,660 --> 00:35:00,660 marginal revenue function. 731 00:35:00,660 --> 00:35:03,710 You calculate your marginal revenue which will be a 732 00:35:03,710 --> 00:35:08,020 function of other firm's quantities. 733 00:35:12,080 --> 00:35:14,740 So your residual demand will lead you to calculate a 734 00:35:14,740 --> 00:35:15,750 marginal revenue function. 735 00:35:15,750 --> 00:35:17,370 It's a function of other firms' quantities. 736 00:35:20,550 --> 00:35:29,860 You then do the same, do one and two for all firms. So for 737 00:35:29,860 --> 00:35:31,960 each firm you end up with a marginal revenue function and 738 00:35:31,960 --> 00:35:33,330 a function of all the firm's quantities. 739 00:35:36,470 --> 00:35:40,230 Step four is you have n equations and n 740 00:35:40,230 --> 00:35:41,615 unknowns and you solve. 741 00:35:47,610 --> 00:35:50,520 So you develop a series of equation where each firm's 742 00:35:50,520 --> 00:35:53,290 marginal revenue function is a function of each other firms 743 00:35:53,290 --> 00:35:54,540 quantities. 744 00:35:54,540 --> 00:35:57,230 You get one equation like that for each firm. 745 00:35:57,230 --> 00:35:59,640 That leaves you n equations and n unknowns you solve. 746 00:35:59,640 --> 00:36:02,370 If you can solve it then you reach equilibrium. 747 00:36:02,370 --> 00:36:04,710 If you don't have a solution then there is no stable Nash 748 00:36:04,710 --> 00:36:05,210 equilibrium. 749 00:36:05,210 --> 00:36:08,400 But if you can solve that there is a Cournot equilibrium 750 00:36:08,400 --> 00:36:10,400 and you solve for it. 751 00:36:10,400 --> 00:36:12,780 So what we're going to do here is I'm going to illustrate 752 00:36:12,780 --> 00:36:16,420 this to you graphically today and we'll work through some 753 00:36:16,420 --> 00:36:19,250 more of the math of it next time. 754 00:36:19,250 --> 00:36:22,780 So we'll start by doing this graphically. 755 00:36:22,780 --> 00:36:27,410 So let's start by considering the case of American Airlines. 756 00:36:27,410 --> 00:36:30,660 Let's start with figure 16-1. 757 00:36:30,660 --> 00:36:32,485 Start by considering the case of American Airlines. 758 00:36:36,580 --> 00:36:43,440 And let's say that the demand curve in this market in our 759 00:36:43,440 --> 00:36:48,590 example we're going to do, let's say that the demand 760 00:36:48,590 --> 00:36:54,320 curve is of the form p equals 339 minus q. 761 00:36:54,320 --> 00:36:59,570 So there's 339,000 flights that are demanded each month. 762 00:36:59,570 --> 00:37:03,140 Each month there are 339,000 flights demanded 763 00:37:03,140 --> 00:37:04,920 in the whole market. 764 00:37:04,920 --> 00:37:06,660 So 339,000 people want to go from New York to 765 00:37:06,660 --> 00:37:09,890 Chicago every month. 766 00:37:09,890 --> 00:37:16,080 And let's also assume the marginal cost is $147. 767 00:37:16,080 --> 00:37:17,790 I don't know where Perloff came up with these numbers, 768 00:37:17,790 --> 00:37:19,460 but let's just go with them. 769 00:37:19,460 --> 00:37:20,740 The specific numbers don't matter. 770 00:37:23,260 --> 00:37:26,470 Now what would American Airlines do if it was a 771 00:37:26,470 --> 00:37:28,180 monopolist? 772 00:37:28,180 --> 00:37:31,540 If American Airlines was a monopolist, it would set 773 00:37:31,540 --> 00:37:38,470 marginal revenues which are 339 minus 2q by the same math 774 00:37:38,470 --> 00:37:39,040 we did before. 775 00:37:39,040 --> 00:37:41,670 You just multiply it through by q and then differentiate 776 00:37:41,670 --> 00:37:45,020 and you get 339 minus 2q equal to the marginal 777 00:37:45,020 --> 00:37:49,850 cost which is 147. 778 00:37:49,850 --> 00:38:00,180 So if it was a monopolist it would choose a quantity of 96 779 00:38:00,180 --> 00:38:07,644 and it would choose a price of $243. 780 00:38:07,644 --> 00:38:10,020 A prices of $243 which we would just get 781 00:38:10,020 --> 00:38:11,150 out the demand curve. 782 00:38:11,150 --> 00:38:14,780 If the quantity is 96, the price is $243. 783 00:38:14,780 --> 00:38:17,830 And that's what we see here. 784 00:38:17,830 --> 00:38:20,820 The marginal revenue curve intersects the marginal cost 785 00:38:20,820 --> 00:38:26,270 curve at a quantity of 96,000. 786 00:38:26,270 --> 00:38:28,540 You then go up to the demand curve to read off the price. 787 00:38:28,540 --> 00:38:29,940 Remember for a monopolist you've got to still respect 788 00:38:29,940 --> 00:38:31,350 the demand curve. 789 00:38:31,350 --> 00:38:32,585 You get the demand curve to read off the 790 00:38:32,585 --> 00:38:34,210 price, that's $243. 791 00:38:34,210 --> 00:38:36,560 That's what American would do if they were monopolist. So if 792 00:38:36,560 --> 00:38:40,350 they were the only folks flying New York to Chicago, 793 00:38:40,350 --> 00:38:47,480 they fly 96,000 people a month at a price of $243,000. 794 00:38:47,480 --> 00:38:50,360 However, now let's say American recognizes that 795 00:38:50,360 --> 00:38:51,970 United is in the market. 796 00:38:51,970 --> 00:38:55,910 And let's say American recognizes that United is 797 00:38:55,910 --> 00:38:58,490 going to deliver some amount of flights q sub u. 798 00:39:01,390 --> 00:39:02,675 They know American is going to do some amount of 799 00:39:02,675 --> 00:39:03,510 flights q sub u. 800 00:39:03,510 --> 00:39:06,150 They don't quite know yet what it is, but they know there's 801 00:39:06,150 --> 00:39:07,400 going to be some amount of flights q sub u. 802 00:39:10,220 --> 00:39:14,640 So the residual demand for American is q sub a equals 803 00:39:14,640 --> 00:39:17,130 total demand minus q sub u. 804 00:39:17,130 --> 00:39:18,480 That's their residual demand. 805 00:39:22,240 --> 00:39:27,370 So, for example, let's say that American just guesses 806 00:39:27,370 --> 00:39:31,140 that United will fly 64,000 passengers. 807 00:39:31,140 --> 00:39:34,050 Let's say Americans says, look, I just know, I've got 808 00:39:34,050 --> 00:39:39,230 some corporate spy who's told me that United will fly 64,000 809 00:39:39,230 --> 00:39:41,830 passengers. 810 00:39:41,830 --> 00:39:44,370 So what you want to do is then you just re-solve the problem 811 00:39:44,370 --> 00:39:46,300 but using residual demand. 812 00:39:46,300 --> 00:39:48,490 So then you say, well if United is going to fly 64,000 813 00:39:48,490 --> 00:39:53,810 passengers then my residual demand is that price equals 814 00:39:53,810 --> 00:40:03,000 339 minus the quantity I sell, q sub a, minus q sub u, which 815 00:40:03,000 --> 00:40:06,400 I think is 64,000, which is 64. 816 00:40:06,400 --> 00:40:17,600 So my new residual demand is p equals 275 minus q sub a. 817 00:40:17,600 --> 00:40:18,720 That's my new residual demand. 818 00:40:18,720 --> 00:40:21,110 Because I thought United is going to sell 64,000. 819 00:40:21,110 --> 00:40:23,520 So instead of my demand being 339 minus q, now 820 00:40:23,520 --> 00:40:26,520 275 minus q sub a. 821 00:40:26,520 --> 00:40:28,970 That's what's left. 822 00:40:28,970 --> 00:40:34,270 So if I use this as my new demand function and re-solve, 823 00:40:34,270 --> 00:40:37,700 if this is my demand function, my marginal revenues are then 824 00:40:37,700 --> 00:40:42,150 275 minus 2 qa. 825 00:40:42,150 --> 00:40:47,010 My marginal cost is the same which is 147. 826 00:40:47,010 --> 00:40:52,530 So instead of my equation being 339 minus 2q equals 147. 827 00:40:52,530 --> 00:40:57,180 Now it's 275 minus 2qa equals 147. 828 00:40:57,180 --> 00:41:06,790 If I do that I'm going to get a qa star of 64,000 flights. 829 00:41:06,790 --> 00:41:10,150 I'm going to say, well look, if I was a monopolist I would 830 00:41:10,150 --> 00:41:12,140 have deliver 96,000 flights. 831 00:41:12,140 --> 00:41:16,560 But given that United is delivering 64,000, that's it's 832 00:41:16,560 --> 00:41:20,030 going to be optimal for me to also deliver 64,000. 833 00:41:20,030 --> 00:41:23,235 At 64,000 flights what's my price going to be? 834 00:41:23,235 --> 00:41:25,730 Well my price is 275 minus qa. 835 00:41:25,730 --> 00:41:31,530 So my price is going be to be $211. 836 00:41:31,530 --> 00:41:34,285 If I think United is delivering 64,000 flights then 837 00:41:34,285 --> 00:41:41,040 I'm going to deliver 64,000 flights at a price of $211. 838 00:41:41,040 --> 00:41:46,110 So that's basically how American would function. 839 00:41:46,110 --> 00:41:48,440 Now what's strange about this is American doesn't know how 840 00:41:48,440 --> 00:41:50,090 many flights United is going to deliver. 841 00:41:50,090 --> 00:41:50,890 There isn't such a thing. 842 00:41:50,890 --> 00:41:53,910 In fact, it's not like there's not some rule which says we're 843 00:41:53,910 --> 00:41:55,390 going to go 64,000. 844 00:41:55,390 --> 00:41:58,530 United is trying to figure this out too. 845 00:41:58,530 --> 00:42:02,730 So, in fact, simultaneously to American making this decision, 846 00:42:02,730 --> 00:42:05,210 United is making the same decision. 847 00:42:05,210 --> 00:42:08,180 And they're going through the exact same math. 848 00:42:08,180 --> 00:42:11,140 They're saying, well gee, given how much American flies, 849 00:42:11,140 --> 00:42:12,390 how much should we fly? 850 00:42:15,040 --> 00:42:16,620 They're going through the same math. 851 00:42:16,620 --> 00:42:23,500 And in fact if we assume that both firms have to face the 852 00:42:23,500 --> 00:42:26,600 same marginal cost and the same demand curve, then in 853 00:42:26,600 --> 00:42:29,970 fact they're solving a symmetric problem. 854 00:42:29,970 --> 00:42:32,380 They are also creating a residual demand function, but 855 00:42:32,380 --> 00:42:36,310 instead of being qa equals d minus qu, now United is making 856 00:42:36,310 --> 00:42:38,850 qu equals d minus qa. 857 00:42:38,850 --> 00:42:41,580 They're making a parallel residual demand function and 858 00:42:41,580 --> 00:42:44,110 they are solving as well. 859 00:42:44,110 --> 00:42:48,600 And both firms, therefore, are ending up with choices of 860 00:42:48,600 --> 00:42:53,310 quantities that depend on the other firm's quantity. 861 00:42:53,310 --> 00:43:00,300 And in particular what they're developing is what we call a 862 00:43:00,300 --> 00:43:01,830 best response curve. 863 00:43:01,830 --> 00:43:04,980 So figure 16-2, I skipped over figure 16-2. 864 00:43:04,980 --> 00:43:10,520 This just illustrates what happens when American thinks 865 00:43:10,520 --> 00:43:11,560 United is committing 64,000. 866 00:43:11,560 --> 00:43:13,060 Let's go through that in one second. 867 00:43:13,060 --> 00:43:15,720 Get through it mathematically. 868 00:43:15,720 --> 00:43:17,630 This is an example where American knows United is doing 869 00:43:17,630 --> 00:43:19,390 64,000 flights. 870 00:43:19,390 --> 00:43:21,860 So they say, well look, my residual demand is essentially 871 00:43:21,860 --> 00:43:24,500 this new line d super r. 872 00:43:24,500 --> 00:43:27,420 And that's what I choose on that new line. 873 00:43:27,420 --> 00:43:31,560 So that creates a new marginal revenue curve, mr super r. 874 00:43:31,560 --> 00:43:34,290 That new marginal revenue curve intersects marginal cost 875 00:43:34,290 --> 00:43:38,250 at 64,000 and that's why I fly only 64,000 flights 876 00:43:38,250 --> 00:43:40,380 at a price of $211. 877 00:43:40,380 --> 00:43:44,395 So you see here is one example of how given an amount United 878 00:43:44,395 --> 00:43:48,760 is flying, how American chooses how much to fly. 879 00:43:48,760 --> 00:43:53,140 Questions about that graphic that ties the math I did here? 880 00:43:53,140 --> 00:43:56,410 What figure 16-3 does is say, look, we can actually do this 881 00:43:56,410 --> 00:43:59,240 for a whole host of possible production levels 882 00:43:59,240 --> 00:44:00,770 by the other firm. 883 00:44:00,770 --> 00:44:05,880 And we can develop what we call best response curves. 884 00:44:05,880 --> 00:44:09,160 Best response curves are, given what the other firm 885 00:44:09,160 --> 00:44:11,290 does, what should I do. 886 00:44:11,290 --> 00:44:17,140 So, for example, American's best response curve is given 887 00:44:17,140 --> 00:44:22,190 that-- so on the x-axis we have how many thousands of 888 00:44:22,190 --> 00:44:27,180 flights American's passengers are flying per quarter. 889 00:44:27,180 --> 00:44:29,290 On the y-axis how many thousands of flights United 890 00:44:29,290 --> 00:44:33,560 passengers are flying per quarter. 891 00:44:33,560 --> 00:44:44,770 So, for example, if American decides to fly zero flights 892 00:44:44,770 --> 00:44:48,410 then United should fly 96 flights, right? 893 00:44:48,410 --> 00:44:51,280 Then United is a monopolist. So that's the point on the 894 00:44:51,280 --> 00:44:55,150 y-axis, to 96,0 point on the curve. 895 00:44:55,150 --> 00:44:57,600 With a 0 on the x-axis, 96 on the y-axis. 896 00:44:57,600 --> 00:45:00,350 If American decides to fly 0. 897 00:45:00,350 --> 00:45:01,580 United should fly 96. 898 00:45:01,580 --> 00:45:04,070 That's the monopoly case we just solved. 899 00:45:04,070 --> 00:45:09,040 If American decides to fly 64, United should fly 64. 900 00:45:09,040 --> 00:45:11,710 That's the case we just solved as well. 901 00:45:11,710 --> 00:45:14,355 Likewise, American's best response curve is 902 00:45:14,355 --> 00:45:15,540 this steeper line. 903 00:45:15,540 --> 00:45:16,730 But it's the same thing. 904 00:45:16,730 --> 00:45:20,790 If United flies 0, American should fly 96 then at 0 on the 905 00:45:20,790 --> 00:45:23,110 y-axis, 96 on the x-axis. 906 00:45:23,110 --> 00:45:28,040 So if United flies 0 American should fly 96. 907 00:45:28,040 --> 00:45:31,770 If United flies 64, American should fly 64. 908 00:45:31,770 --> 00:45:35,680 So you can actually, literally trace out these curves asking 909 00:45:35,680 --> 00:45:38,770 at every single point, given what the other guy's doing, 910 00:45:38,770 --> 00:45:41,020 what should I do. 911 00:45:41,020 --> 00:45:43,410 So we solved for two points on this curve. 912 00:45:43,410 --> 00:45:46,570 We solved for the other guy producing zero point, which is 913 00:45:46,570 --> 00:45:48,250 you produce 96. 914 00:45:48,250 --> 00:45:50,470 We solved for the other guy producing 64 point which is 915 00:45:50,470 --> 00:45:51,820 you produce 64. 916 00:45:51,820 --> 00:45:53,540 That same math can be used to solve for every 917 00:45:53,540 --> 00:45:55,300 point on this curve. 918 00:45:55,300 --> 00:45:55,780 Yeah? 919 00:45:55,780 --> 00:45:56,750 AUDIENCE: [INAUDIBLE] 920 00:45:56,750 --> 00:45:57,235 192 point. 921 00:45:57,235 --> 00:46:00,330 PROFESSOR: The 192 point is it's the 922 00:46:00,330 --> 00:46:01,630 question is the following. 923 00:46:01,630 --> 00:46:08,560 At what point would American produce zero. 924 00:46:08,560 --> 00:46:10,855 How much when United have to produce for American to 925 00:46:10,855 --> 00:46:11,540 produce zero. 926 00:46:11,540 --> 00:46:12,630 Well they'd only produce zero if United 927 00:46:12,630 --> 00:46:16,300 was producing 192,000. 928 00:46:16,300 --> 00:46:18,980 Only at that point would they actually say, forget it, we're 929 00:46:18,980 --> 00:46:22,730 just going to produce zero. 930 00:46:22,730 --> 00:46:26,000 That's what the 192 point means. 931 00:46:26,000 --> 00:46:28,780 Only if they knew United was producing all that much would 932 00:46:28,780 --> 00:46:31,150 they just drop out of the market. 933 00:46:31,150 --> 00:46:33,440 So that's the 192 intersection. 934 00:46:33,440 --> 00:46:35,890 A backwards way to read the curves. 935 00:46:35,890 --> 00:46:39,480 But the bottom line, is essentially we can write these 936 00:46:39,480 --> 00:46:40,760 best response curves. 937 00:46:43,490 --> 00:46:47,520 They're basically the quantity I'm going to produce given the 938 00:46:47,520 --> 00:46:49,980 quantity the other firm produces. 939 00:46:49,980 --> 00:46:52,430 And the key thing is that these are 940 00:46:52,430 --> 00:46:55,030 symmetric in this example. 941 00:46:55,030 --> 00:46:59,180 Since the costs are the same and they both face the same 942 00:46:59,180 --> 00:47:03,540 market demand then these curves are symmetric. 943 00:47:07,380 --> 00:47:12,680 What that means is that these curves are having figured out 944 00:47:12,680 --> 00:47:16,020 one you can automatically draw the other. 945 00:47:16,020 --> 00:47:18,500 A trick for solving these problems is that if you have a 946 00:47:18,500 --> 00:47:21,490 symmetric Cournot equilibrium you don't need to calculate 947 00:47:21,490 --> 00:47:23,560 the math to find each firm's best response curve. 948 00:47:23,560 --> 00:47:26,080 Once you calculate one you know the other firm's just a 949 00:47:26,080 --> 00:47:27,570 complement of it. 950 00:47:27,570 --> 00:47:30,030 So having calculated American's best response curve 951 00:47:30,030 --> 00:47:32,590 we could have automatically drawn the United best response 952 00:47:32,590 --> 00:47:36,010 curve as a complement of that. 953 00:47:36,010 --> 00:47:39,500 The other key point is by drawing this diagram we can 954 00:47:39,500 --> 00:47:41,820 see the Cournot equilibrium. 955 00:47:41,820 --> 00:47:43,690 Remember Cournot equilibrium. 956 00:47:43,690 --> 00:47:47,930 Cournot equilibrium is where I'm happy with my quantity 957 00:47:47,930 --> 00:47:49,840 given what the other firm's doing. 958 00:47:49,840 --> 00:47:50,940 Given what the other firm's doing I can't 959 00:47:50,940 --> 00:47:52,280 make any more money. 960 00:47:52,280 --> 00:47:53,665 Once again, I don't care about market share, I just care 961 00:47:53,665 --> 00:47:54,860 about money. 962 00:47:54,860 --> 00:47:56,480 So given what the other firm's doing I can't 963 00:47:56,480 --> 00:47:57,480 make any more money. 964 00:47:57,480 --> 00:48:02,650 Well that happens at 64,000 each. 965 00:48:02,650 --> 00:48:05,920 Because when American is producing 64,000, United is 966 00:48:05,920 --> 00:48:07,540 happy to produce 64,000. 967 00:48:07,540 --> 00:48:09,590 That's their profit maximizing choice. 968 00:48:09,590 --> 00:48:11,530 If United is producing 64,000 American's 969 00:48:11,530 --> 00:48:12,860 happy to produce 64,000. 970 00:48:12,860 --> 00:48:15,110 That's their profit maximizing choice. 971 00:48:15,110 --> 00:48:18,500 So that point of each producing 64,000 we are in a 972 00:48:18,500 --> 00:48:20,630 Nash or Cournot equilibrium. 973 00:48:20,630 --> 00:48:23,780 Both firms are happy given what the other firm is doing. 974 00:48:23,780 --> 00:48:26,290 Both firms are profit maximizing given what the 975 00:48:26,290 --> 00:48:27,540 other firm is doing. 976 00:48:29,850 --> 00:48:33,630 Now basically, for example, another way to look at this is 977 00:48:33,630 --> 00:48:37,310 that you're only in equilibrium if you're on both 978 00:48:37,310 --> 00:48:39,390 firms' reaction curves. 979 00:48:39,390 --> 00:48:43,860 So, for example, American might say, look the 980 00:48:43,860 --> 00:48:47,060 equilibrium I like is where I do 96,000 981 00:48:47,060 --> 00:48:49,710 flights and you none. 982 00:48:49,710 --> 00:48:54,980 So the equilibrium I like is on the x-axis the point 96, 0, 983 00:48:54,980 --> 00:48:58,160 where I do 96,000 flights and you United do none. 984 00:48:58,160 --> 00:49:02,070 United says, however, no that's not optimal for me. 985 00:49:02,070 --> 00:49:03,480 Because if you're doing that, then you're 986 00:49:03,480 --> 00:49:07,000 charging a price of $243. 987 00:49:07,000 --> 00:49:08,170 So there's money to be made for me. 988 00:49:08,170 --> 00:49:10,570 I can come in and start stealing some of your flights. 989 00:49:10,570 --> 00:49:12,560 So that's not an equilibrium from my perspective. 990 00:49:12,560 --> 00:49:13,790 Might be an equilibrium from your perspective. 991 00:49:13,790 --> 00:49:15,820 You're delighted you're a monopolist. But not from my 992 00:49:15,820 --> 00:49:16,630 perspective. 993 00:49:16,630 --> 00:49:17,940 At that price I'll come in and start 994 00:49:17,940 --> 00:49:19,850 stealing some your business. 995 00:49:19,850 --> 00:49:20,670 And I'm going to start stealing 996 00:49:20,670 --> 00:49:21,190 some of your business. 997 00:49:21,190 --> 00:49:24,500 As I steal your business you are going to have to move up 998 00:49:24,500 --> 00:49:29,670 your best response curve because your residual demand 999 00:49:29,670 --> 00:49:30,890 is shrinking. 1000 00:49:30,890 --> 00:49:32,950 And you'll only reach equilibrium when you're both 1001 00:49:32,950 --> 00:49:33,830 happy with the outcome. 1002 00:49:33,830 --> 00:49:35,695 If only one firm is happy with the outcome the other firm can 1003 00:49:35,695 --> 00:49:38,200 always change its behavior, raise its price up or down or 1004 00:49:38,200 --> 00:49:40,700 its quantity up or down to change the market share and 1005 00:49:40,700 --> 00:49:41,820 change the outcome. 1006 00:49:41,820 --> 00:49:44,330 So equilibrium will only be when you're at both firms best 1007 00:49:44,330 --> 00:49:45,340 response curves. 1008 00:49:45,340 --> 00:49:46,980 You'll only be at both firm's best response curves where 1009 00:49:46,980 --> 00:49:49,270 they intersect. 1010 00:49:49,270 --> 00:49:51,290 Let's stop there I'm going to come back next time. 1011 00:49:53,820 --> 00:49:56,070 Jessica we should have the same handout next time. 1012 00:49:56,070 --> 00:49:57,690 Let's make sure this figure is in the handout 1013 00:49:57,690 --> 00:49:59,670 next time as well. 1014 00:49:59,670 --> 00:50:01,670 And we'll come back and talk about this last figure and 1015 00:50:01,670 --> 00:50:03,010 we'll do the math behind it as well.