1 00:00:00,960 --> 00:00:01,920 [SQUEAKING] 2 00:00:01,920 --> 00:00:03,840 [RUSTLING] 3 00:00:03,840 --> 00:00:11,520 [CLICKING] 4 00:00:11,520 --> 00:00:14,400 JONATHAN GRUBER: All right, why don't we get started? 5 00:00:14,400 --> 00:00:18,600 Today we're going to move on to, finally, the most 6 00:00:18,600 --> 00:00:20,340 realistic market structure. 7 00:00:20,340 --> 00:00:22,260 We talked about perfectly competitive markets. 8 00:00:22,260 --> 00:00:25,680 Now, that was a very useful, extreme example 9 00:00:25,680 --> 00:00:27,952 to help us think about economic efficiency. 10 00:00:27,952 --> 00:00:29,910 We then flipped over to talk about the somewhat 11 00:00:29,910 --> 00:00:32,009 more real estate case of monopoly, 12 00:00:32,009 --> 00:00:35,550 but still, very few markets have only one participant. 13 00:00:35,550 --> 00:00:38,940 A true monopoly is rare in the private market. 14 00:00:38,940 --> 00:00:42,000 What most markets are marked by are probably 15 00:00:42,000 --> 00:00:44,580 more features of oligopoly, which 16 00:00:44,580 --> 00:00:48,840 is a market with a small group of firms competing 17 00:00:48,840 --> 00:00:52,980 with each other, but with barriers to entry that keep out 18 00:00:52,980 --> 00:00:54,833 an unlimited number of firms. 19 00:00:54,833 --> 00:00:56,250 Think about these as markets where 20 00:00:56,250 --> 00:00:57,990 there are some barriers to entry, 21 00:00:57,990 --> 00:01:00,270 so firms just can't consciously enter and exit 22 00:01:00,270 --> 00:01:03,570 like they could in our IBM/Dell example, 23 00:01:03,570 --> 00:01:06,180 but where there's small enough barriers to entry 24 00:01:06,180 --> 00:01:08,788 that a few firms have gotten in, not just one. 25 00:01:08,788 --> 00:01:10,080 So it's not a natural monopoly. 26 00:01:10,080 --> 00:01:12,270 It's not like only one firm can be in there. 27 00:01:12,270 --> 00:01:14,030 Multiple firms are in there, but they only 28 00:01:14,030 --> 00:01:15,780 know they have to compete with each other, 29 00:01:15,780 --> 00:01:18,600 not with the big, wide world. 30 00:01:18,600 --> 00:01:20,200 So for example, the classic example 31 00:01:20,200 --> 00:01:24,060 of an oligopoly industry would be the auto industry. 32 00:01:24,060 --> 00:01:26,393 Auto manufacturers clearly compete. 33 00:01:26,393 --> 00:01:27,810 Clearly, if you watch any sporting 34 00:01:27,810 --> 00:01:29,520 event and watch how much advertising that goes, 35 00:01:29,520 --> 00:01:31,270 they're clearly competing with each other. 36 00:01:31,270 --> 00:01:33,900 They're comparing to each other all the time. 37 00:01:33,900 --> 00:01:37,110 But most of the cars in the world 38 00:01:37,110 --> 00:01:39,660 are produced by fewer than 10 auto manufacturers. 39 00:01:39,660 --> 00:01:41,910 The notion that we have a perfectly competitive market 40 00:01:41,910 --> 00:01:44,940 of thousands of sellers selling identical goods 41 00:01:44,940 --> 00:01:48,290 is clearly not right when it comes to buying a car. 42 00:01:48,290 --> 00:01:50,830 So that's the model we're going to want to focus on 43 00:01:50,830 --> 00:01:52,820 for the next few lectures. 44 00:01:52,820 --> 00:01:59,992 Now, within an oligopoly market, whenever 45 00:01:59,992 --> 00:02:01,450 we think about this market, we want 46 00:02:01,450 --> 00:02:03,910 to start by noting that within this market, 47 00:02:03,910 --> 00:02:05,740 these limited sets of competitors 48 00:02:05,740 --> 00:02:07,730 can behave in two ways. 49 00:02:07,730 --> 00:02:15,170 They can behave cooperatively or non-cooperatively. 50 00:02:19,660 --> 00:02:22,930 Cooperatively means that they can 51 00:02:22,930 --> 00:02:27,250 form what's called a cartel. 52 00:02:27,250 --> 00:02:30,270 So when there's an oligopoly market 53 00:02:30,270 --> 00:02:34,380 and the firms cooperatively get together and make decisions, 54 00:02:34,380 --> 00:02:38,250 that's called the cartel, the most famous example of which 55 00:02:38,250 --> 00:02:43,130 is OPEC, the Organization of Petroleum Exporting Countries, 56 00:02:43,130 --> 00:02:45,860 which are the set of countries that control about 2/3 57 00:02:45,860 --> 00:02:49,830 of the world's oil, led by Saudi Arabia, 58 00:02:49,830 --> 00:02:54,140 is the major player in OPEC. 59 00:02:54,140 --> 00:02:57,080 It's a cartel of about a dozen nations. 60 00:02:57,080 --> 00:03:00,170 And what they do is they control the vast majority 61 00:03:00,170 --> 00:03:02,270 of the world's oil reserves. 62 00:03:02,270 --> 00:03:04,970 And by behaving cooperatively, they essentially 63 00:03:04,970 --> 00:03:07,610 turn themselves into a monopoly. 64 00:03:07,610 --> 00:03:10,550 OPEC acts as if they've got the monopoly in oil. 65 00:03:10,550 --> 00:03:14,770 Certainly they used to. 66 00:03:14,770 --> 00:03:15,770 Now it's getting harder. 67 00:03:15,770 --> 00:03:18,180 Other non-OPEC countries are starting to produce more oil 68 00:03:18,180 --> 00:03:19,610 and it's breaking down. 69 00:03:19,610 --> 00:03:21,590 But for a long time, they were essentially 70 00:03:21,590 --> 00:03:23,577 the cooperative producer of oil, and act 71 00:03:23,577 --> 00:03:25,910 essential like a monopoly, and they made lots of profits 72 00:03:25,910 --> 00:03:26,890 like a monopoly. 73 00:03:26,890 --> 00:03:30,413 That kept prices high, they kept production inefficiently low, 74 00:03:30,413 --> 00:03:31,580 and they made lots of money. 75 00:03:34,410 --> 00:03:37,783 However, that's a great outcome for producers, 76 00:03:37,783 --> 00:03:39,200 but as we'll talk about next time, 77 00:03:39,200 --> 00:03:41,430 it's actually a hard outcome to enforce. 78 00:03:41,430 --> 00:03:44,120 Turns out to be hard to keep cartels together. 79 00:03:44,120 --> 00:03:46,490 And so typically, oligopoly markets 80 00:03:46,490 --> 00:03:50,130 behave in a non-cooperative way, with the participants 81 00:03:50,130 --> 00:03:53,750 competing with each other, not cooperating with each other. 82 00:03:53,750 --> 00:03:57,060 In this case, you can actually get them driving their profits 83 00:03:57,060 --> 00:03:59,970 down far below the monopoly level, 84 00:03:59,970 --> 00:04:03,610 and indeed, perhaps even all the way to the competitive level. 85 00:04:03,610 --> 00:04:05,860 So you can think about markets as a competitive as one 86 00:04:05,860 --> 00:04:08,260 extreme and the monopoly as the other extreme, 87 00:04:08,260 --> 00:04:10,090 oligopoly in between. 88 00:04:10,090 --> 00:04:12,250 A cooperative oligopoly market, like cartel, 89 00:04:12,250 --> 00:04:15,940 will end up close to the monopoly outcome. 90 00:04:15,940 --> 00:04:18,998 A non-cooperative market will end up somewhere in between, 91 00:04:18,998 --> 00:04:21,040 and we're going to model today's where in between 92 00:04:21,040 --> 00:04:24,010 do they end up. 93 00:04:24,010 --> 00:04:25,820 Now, to think about this, we're going 94 00:04:25,820 --> 00:04:28,090 to have to turn to a tool, which has really 95 00:04:28,090 --> 00:04:30,460 become a dominant tool in economics over the last 40 96 00:04:30,460 --> 00:04:33,370 years, which is the tool of game theory. 97 00:04:39,590 --> 00:04:41,390 Game theory. 98 00:04:41,390 --> 00:04:46,060 So basically, we're going to think of oligopoly firms 99 00:04:46,060 --> 00:04:49,700 as engaging in a game. 100 00:04:49,700 --> 00:04:57,210 And as with any game, you need to know two things. 101 00:04:57,210 --> 00:05:03,090 One is you need to what's the strategy, 102 00:05:03,090 --> 00:05:06,610 and the second is you need to know when is the game over. 103 00:05:06,610 --> 00:05:08,326 What's the equilibrium? 104 00:05:12,790 --> 00:05:17,590 And that's, essentially, what you do with any game. 105 00:05:17,590 --> 00:05:22,870 And so basically, the key with game theory 106 00:05:22,870 --> 00:05:26,290 is that we are going to find the equilibrium, 107 00:05:26,290 --> 00:05:28,330 and that's going to yield for us the strategy 108 00:05:28,330 --> 00:05:30,950 that players are going to use. 109 00:05:30,950 --> 00:05:33,295 However, equilibrium in a game is not well-defined. 110 00:05:33,295 --> 00:05:34,670 It's not like a set of rules that 111 00:05:34,670 --> 00:05:36,380 are printed out, like monopoly. 112 00:05:36,380 --> 00:05:39,550 In a non-cooperative oligopoly market, the equilibrium, 113 00:05:39,550 --> 00:05:42,050 you have to actually come up with different concepts of what 114 00:05:42,050 --> 00:05:42,770 equilibrium is. 115 00:05:42,770 --> 00:05:45,470 There's not a hard and fast scientific rule. 116 00:05:45,470 --> 00:05:47,450 And the typical one that's used is 117 00:05:47,450 --> 00:05:57,140 called the Nash equilibrium, the Nash equilibrium, 118 00:05:57,140 --> 00:06:02,188 named for John Nash, the famous mathematician, who economists 119 00:06:02,188 --> 00:06:04,355 have claimed as their own, even though he was really 120 00:06:04,355 --> 00:06:05,230 a mathematician. 121 00:06:05,230 --> 00:06:07,760 But we gave him the Nobel Prize anyway. 122 00:06:07,760 --> 00:06:09,590 And if you think of economists, probably 123 00:06:09,590 --> 00:06:11,757 one of the most famous, you all know about the movie 124 00:06:11,757 --> 00:06:14,510 and book Beautiful Mind. 125 00:06:14,510 --> 00:06:19,720 He is based on the father of game theory. 126 00:06:19,720 --> 00:06:23,290 So basically, what is the Nash equilibrium? 127 00:06:23,290 --> 00:06:30,220 The Nash equilibrium is defined as the point at which no player 128 00:06:30,220 --> 00:06:33,520 wants to change their strategy, given what 129 00:06:33,520 --> 00:06:36,580 the other players are doing. 130 00:06:36,580 --> 00:06:40,710 So the point at which no player wants to change its strategy, 131 00:06:40,710 --> 00:06:43,490 given what the other players are doing. 132 00:06:43,490 --> 00:06:47,480 So in other words, every player is happy with where they are. 133 00:06:47,480 --> 00:06:49,490 Given what every other player's decided, 134 00:06:49,490 --> 00:06:51,410 I'm happy to do what I've decided. 135 00:06:51,410 --> 00:06:54,350 So I've got a strategy, and given the strategy 136 00:06:54,350 --> 00:06:58,250 other players are using, if I'm happy with my strategy, then 137 00:06:58,250 --> 00:07:01,640 that's in equilibrium. 138 00:07:01,640 --> 00:07:04,120 So this is a super abstract concept, 139 00:07:04,120 --> 00:07:06,340 so let's illustrate it with an example. 140 00:07:06,340 --> 00:07:09,040 And the classic example of game theory 141 00:07:09,040 --> 00:07:15,350 is the prisoner's dilemma, which many of you, I'm sure, 142 00:07:15,350 --> 00:07:18,362 know about, maybe the most of you, 143 00:07:18,362 --> 00:07:19,570 but let's just go through it. 144 00:07:19,570 --> 00:07:22,210 This is the thing from the old cop movies you see, 145 00:07:22,210 --> 00:07:27,730 where they arrest two guys and they put them in separate rooms 146 00:07:27,730 --> 00:07:29,920 and they basically interrogate them separately. 147 00:07:32,940 --> 00:07:36,042 They're put in separate rooms, and let's say that these guys 148 00:07:36,042 --> 00:07:37,000 get told the following. 149 00:07:37,000 --> 00:07:39,670 They each get told separately the following thing. 150 00:07:39,670 --> 00:07:44,410 They get told that right now, if nothing else happens, 151 00:07:44,410 --> 00:07:48,260 there's enough evidence to send them each away for one year. 152 00:07:48,260 --> 00:07:55,000 However, they're told, if they turned on their friend 153 00:07:55,000 --> 00:07:58,000 and say their friend's guilty, then they go free 154 00:07:58,000 --> 00:08:00,620 and their friend gets five years. 155 00:08:00,620 --> 00:08:04,010 If their friend turns on them, then the friend goes free 156 00:08:04,010 --> 00:08:05,820 and they get five years. 157 00:08:05,820 --> 00:08:10,500 But if they both turn on each other, they both get two years. 158 00:08:10,500 --> 00:08:13,590 Set up as if they both stay silent, they both get one year. 159 00:08:13,590 --> 00:08:16,380 If one turns, then that person gets to leave 160 00:08:16,380 --> 00:08:18,070 and the person gets five years. 161 00:08:18,070 --> 00:08:22,250 But if they both turn, then they each get two years. 162 00:08:22,250 --> 00:08:24,040 So how do we think about decision-making 163 00:08:24,040 --> 00:08:25,010 in that context? 164 00:08:25,010 --> 00:08:28,720 The way we do that is we write down, we call, a payoff matrix. 165 00:08:28,720 --> 00:08:31,690 We write down in matrix form this decision. 166 00:08:31,690 --> 00:08:33,940 So let's think about what a playoff matrix looks like. 167 00:08:33,940 --> 00:08:37,809 Up here is prisoner B, and here you 168 00:08:37,809 --> 00:08:48,020 have prisoner A. Prisoner A. And prisoner A can remain silent 169 00:08:48,020 --> 00:08:54,210 or they can talk, and prisoner B can remain silent 170 00:08:54,210 --> 00:08:55,080 or they can talk. 171 00:08:57,980 --> 00:08:59,390 And then we just write down, what 172 00:08:59,390 --> 00:09:01,760 are the outcomes, or the payoffs, 173 00:09:01,760 --> 00:09:03,932 from these different strategies? 174 00:09:03,932 --> 00:09:07,190 So prisoner A says nothing and prisoner B says nothing, 175 00:09:07,190 --> 00:09:11,900 then A gets one year and B gets one year. 176 00:09:11,900 --> 00:09:15,290 If prisoner A says nothing and prisoner B says, oh yeah, 177 00:09:15,290 --> 00:09:17,360 prisoner A is definitely guilty, then 178 00:09:17,360 --> 00:09:21,620 prisoner A gets five years and prisoner gets zero years. 179 00:09:24,480 --> 00:09:26,230 If the opposite happens, if prison A says, 180 00:09:26,230 --> 00:09:29,170 yeah, B's guilty, and B doesn't say anything about A, 181 00:09:29,170 --> 00:09:33,980 then A gets zero years and B gets five years. 182 00:09:33,980 --> 00:09:36,212 But if they both say the other one's guilty, 183 00:09:36,212 --> 00:09:37,420 then they each get two years. 184 00:09:40,430 --> 00:09:42,095 OK, that's the payoff matrix. 185 00:09:45,300 --> 00:09:49,320 And now we want to ask, given this payoff matrix, 186 00:09:49,320 --> 00:09:53,820 what is the right strategy for each prisoner to pursue? 187 00:09:53,820 --> 00:09:56,730 And the way we do this in the Nash equilibrium concept is we 188 00:09:56,730 --> 00:09:59,940 look for a dominant strategy. 189 00:09:59,940 --> 00:10:04,520 Is there a strategy that I would pursue regardless 190 00:10:04,520 --> 00:10:06,913 of what the other person does? 191 00:10:06,913 --> 00:10:08,330 And if there is, I'll pursue that. 192 00:10:08,330 --> 00:10:10,247 Because remember, the Nash equilibrium concept 193 00:10:10,247 --> 00:10:13,010 is, what do I want to do, given what the other person is doing? 194 00:10:13,010 --> 00:10:14,802 If I have a strategy I want to do no matter 195 00:10:14,802 --> 00:10:17,050 what the other person is doing, then I'll do it. 196 00:10:17,050 --> 00:10:19,790 So when asked, is there a dominant strategy? 197 00:10:19,790 --> 00:10:22,960 Is there a strategy that is the best thing to do, no matter 198 00:10:22,960 --> 00:10:26,210 what the other guy does? 199 00:10:26,210 --> 00:10:29,765 Well, clearly, if they're cooperating, 200 00:10:29,765 --> 00:10:32,390 if these were stupid police and they sat them in the same room, 201 00:10:32,390 --> 00:10:35,170 told them and then left, the two guys could cooperate. 202 00:10:35,170 --> 00:10:37,810 Well, clearly, the dominant cooperative strategy 203 00:10:37,810 --> 00:10:40,485 is for both of us to remain silent. 204 00:10:40,485 --> 00:10:42,110 That's the dominant cooperate strategy. 205 00:10:42,110 --> 00:10:44,420 And as a team, we only get two total years 206 00:10:44,420 --> 00:10:47,360 in jail, where everything gets many more years in jail. 207 00:10:47,360 --> 00:10:50,000 So if they're buddies and they trust each other 208 00:10:50,000 --> 00:10:53,022 and they cooperate, then that's clearly the right strategy. 209 00:10:53,022 --> 00:10:54,980 But let's say the police are smart and put them 210 00:10:54,980 --> 00:10:57,850 in separate rooms. 211 00:10:57,850 --> 00:11:02,290 Well, what's the dominant non-cooperative strategy? 212 00:11:02,290 --> 00:11:05,690 What is the strategy that A or B, say A, should produce? 213 00:11:05,690 --> 00:11:07,000 Yeah? 214 00:11:07,000 --> 00:11:08,020 Why? 215 00:11:08,020 --> 00:11:09,490 AUDIENCE: Either way, you're going to get less years. 216 00:11:09,490 --> 00:11:11,615 Like if you're the only person silent and you talk, 217 00:11:11,615 --> 00:11:14,170 you get zero, and if they talk and you talk, 218 00:11:14,170 --> 00:11:15,468 you only get two versus five. 219 00:11:15,468 --> 00:11:16,510 JONATHAN GRUBER: Exactly. 220 00:11:16,510 --> 00:11:20,240 For prisoner A in this first row-- 221 00:11:20,240 --> 00:11:22,050 compare the first column. 222 00:11:22,050 --> 00:11:24,240 We'll say prisoner B is silent. 223 00:11:24,240 --> 00:11:26,250 Then clearly, you're better off talking than not 224 00:11:26,250 --> 00:11:28,420 talking, zero rather than one. 225 00:11:28,420 --> 00:11:30,240 Let's say prisoner B talks. 226 00:11:30,240 --> 00:11:32,880 Then you're still better off talking than not talking. 227 00:11:32,880 --> 00:11:36,750 So no matter what B does, you should talk. 228 00:11:36,750 --> 00:11:41,190 Likewise, prisoner B, no matter what A does, B should talk. 229 00:11:41,190 --> 00:11:42,870 So the non-cooperative equilibrium 230 00:11:42,870 --> 00:11:45,450 is actually this outcome. 231 00:11:45,450 --> 00:11:47,280 They both end up talking. 232 00:11:47,280 --> 00:11:50,400 You get sort of a race to the bottom. 233 00:11:50,400 --> 00:11:52,222 The non-cooperative outcome is much worse 234 00:11:52,222 --> 00:11:53,680 than if they could have cooperated. 235 00:11:56,900 --> 00:11:59,360 So basically, what you get is that 236 00:11:59,360 --> 00:12:02,120 the non-cooperative equilibrium is always 237 00:12:02,120 --> 00:12:06,810 worse for the players than the cooperative equilibrium. 238 00:12:06,810 --> 00:12:11,940 And this was like an unbelievable insight of Nash. 239 00:12:11,940 --> 00:12:14,880 Before Nash, we always thought competition 240 00:12:14,880 --> 00:12:16,640 was always and everywhere good. 241 00:12:16,640 --> 00:12:18,990 We always thought more competition is better, 242 00:12:18,990 --> 00:12:21,300 for the reasons we talked in the first 10 or 12 243 00:12:21,300 --> 00:12:23,190 lectures of this class. 244 00:12:23,190 --> 00:12:25,112 Nash was the first one to say, no, actually, 245 00:12:25,112 --> 00:12:26,070 competition can be bad. 246 00:12:26,070 --> 00:12:27,153 Cooperation can be better. 247 00:12:27,153 --> 00:12:29,670 I don't know if you remember the scene in a Beautiful Mind 248 00:12:29,670 --> 00:12:31,650 where they're picking up girls in the bar. 249 00:12:31,650 --> 00:12:35,670 And he described basically a Nash strategy, 250 00:12:35,670 --> 00:12:39,070 how competition will lead to the worst outcome. 251 00:12:39,070 --> 00:12:41,180 And basically, that's what you see here, 252 00:12:41,180 --> 00:12:43,465 that competition can actually lead to a worse 253 00:12:43,465 --> 00:12:45,340 outcome than cooperation, and that was really 254 00:12:45,340 --> 00:12:48,900 Nash's brilliant insight. 255 00:12:48,900 --> 00:12:57,660 Now, this is a cute example with prisoners, but actually-- 256 00:12:57,660 --> 00:12:59,000 well first, two points. 257 00:12:59,000 --> 00:13:01,260 First of all, this generally shows you 258 00:13:01,260 --> 00:13:05,070 how you do gain favor with Nash equilibrium. 259 00:13:05,070 --> 00:13:08,040 Basically, you look at the payoff matrix, 260 00:13:08,040 --> 00:13:10,860 you find the dominant strategy, and then 261 00:13:10,860 --> 00:13:14,710 you find where those dominant strategies intersect. 262 00:13:14,710 --> 00:13:16,210 And here, the dominant strategies 263 00:13:16,210 --> 00:13:18,040 intersect at this cell, therefore 264 00:13:18,040 --> 00:13:20,990 that's the equilibrium. 265 00:13:20,990 --> 00:13:23,860 So that's basically how you do game theory in a game theory 266 00:13:23,860 --> 00:13:25,850 kindergarten level. 267 00:13:25,850 --> 00:13:26,930 You look at the matrix. 268 00:13:26,930 --> 00:13:29,090 You find each player's dominant strategy. 269 00:13:29,090 --> 00:13:31,700 And you find the point at which those dominant strategies 270 00:13:31,700 --> 00:13:36,160 intersect, and at that point, that's the equilibrium. 271 00:13:36,160 --> 00:13:40,710 Now, that's all well and good for a simple example like this, 272 00:13:40,710 --> 00:13:43,410 but let's actually apply to an economics example. 273 00:13:43,410 --> 00:13:45,690 Let's think about advertising. 274 00:13:45,690 --> 00:13:47,160 So think about Coke and Pepsi. 275 00:13:51,120 --> 00:13:55,230 Right now, let's think about their decision to advertise. 276 00:13:55,230 --> 00:13:56,910 Now, obviously it's a simple problem. 277 00:13:56,910 --> 00:13:59,130 Obviously Pepsi should just be illegal 278 00:13:59,130 --> 00:14:00,370 because Coke is way better. 279 00:14:00,370 --> 00:14:03,330 But sadly, it's not, and sometimes I have to drink Pepsi 280 00:14:03,330 --> 00:14:04,770 and I'm very sad. 281 00:14:04,770 --> 00:14:08,010 But nonetheless, in the real world, we have Coke and Pepsi 282 00:14:08,010 --> 00:14:10,230 and they have to decide how much to advertise. 283 00:14:10,230 --> 00:14:14,130 Now, the dominant cooperative strategy 284 00:14:14,130 --> 00:14:16,770 would be to say, look, advertising 285 00:14:16,770 --> 00:14:18,820 costs us a ton of money. 286 00:14:18,820 --> 00:14:20,430 Let's just split the market. 287 00:14:20,430 --> 00:14:22,722 Let's have a monopoly market and just split it. 288 00:14:22,722 --> 00:14:24,180 We're close to splitting it anyway. 289 00:14:24,180 --> 00:14:25,130 Coke's got some more of it. 290 00:14:25,130 --> 00:14:25,830 We're close to splitting it. 291 00:14:25,830 --> 00:14:26,460 Let's just split it. 292 00:14:26,460 --> 00:14:27,115 Yeah? 293 00:14:27,115 --> 00:14:28,815 AUDIENCE: Can you actually do that? 294 00:14:28,815 --> 00:14:30,070 JONATHAN GRUBER: What? 295 00:14:30,070 --> 00:14:30,280 AUDIENCE: Can you actually do that? 296 00:14:30,280 --> 00:14:31,070 Because I remember, there were places 297 00:14:31,070 --> 00:14:32,590 that you get where you aren't allowed 298 00:14:32,590 --> 00:14:33,630 to sell in the same place. 299 00:14:33,630 --> 00:14:36,255 JONATHAN GRUBER: OK, but that's different than the cooperative. 300 00:14:36,255 --> 00:14:38,810 That's imposed not by Coke and Pepsi jointly. 301 00:14:38,810 --> 00:14:41,180 That's imposed by Pepsi saying to a university campus, 302 00:14:41,180 --> 00:14:45,050 for example, we will cut you a better deal 303 00:14:45,050 --> 00:14:46,882 if you'll agree not to sell Coke. 304 00:14:46,882 --> 00:14:47,840 That's not cooperation. 305 00:14:47,840 --> 00:14:49,760 That's competition. 306 00:14:49,760 --> 00:14:51,300 So there's cooperative strategy. 307 00:14:51,300 --> 00:14:53,660 What if they don't cooperate? 308 00:14:53,660 --> 00:14:58,460 Well, let's imagine we have the following payoff matrix. 309 00:14:58,460 --> 00:15:03,630 You've got Pepsi up here, and they can advertise or not 310 00:15:03,630 --> 00:15:04,860 advertise. 311 00:15:04,860 --> 00:15:10,490 And you've got Coke here, and they can advertise or not 312 00:15:10,490 --> 00:15:12,260 advertise. 313 00:15:12,260 --> 00:15:14,485 And let's say the payoff matrix is the following. 314 00:15:20,420 --> 00:15:23,480 Let's say the total amount of profit to be made 315 00:15:23,480 --> 00:15:25,640 is 16 whatever, billion, whatever 316 00:15:25,640 --> 00:15:28,670 units you want to make it, $16 billion. 317 00:15:28,670 --> 00:15:32,100 And let's say if there's no advertising, Coke gets 8 318 00:15:32,100 --> 00:15:33,717 and Pepsi gets 8. 319 00:15:38,850 --> 00:15:43,370 But let's say advertising costs money. 320 00:15:43,370 --> 00:15:46,700 It costs 5, $5 billion. 321 00:15:46,700 --> 00:15:49,340 So let's say if they both advertise, 322 00:15:49,340 --> 00:15:51,620 then they still end up splitting the market, 323 00:15:51,620 --> 00:15:53,550 but they only make 3. 324 00:15:53,550 --> 00:15:55,370 C equals 3, P equals 3. 325 00:15:59,470 --> 00:16:02,540 I'm sorry, advertise. yes, you're right. 326 00:16:02,540 --> 00:16:06,230 C equals 3, P equals 3. 327 00:16:06,230 --> 00:16:08,425 And here C equals 8, P equals 8. 328 00:16:16,080 --> 00:16:17,880 So basically, you have a situation 329 00:16:17,880 --> 00:16:22,200 where they both end of splitting the market either way, 330 00:16:22,200 --> 00:16:25,590 but they just split a smaller net profit if they advertise. 331 00:16:25,590 --> 00:16:28,290 So clearly, they'd rather be here than here. 332 00:16:28,290 --> 00:16:30,330 But what happens in the off diagonal elements? 333 00:16:30,330 --> 00:16:35,220 Well, let's say also that if Coke advertises but Pepsi does 334 00:16:35,220 --> 00:16:40,050 not, then let's say Coke ends up making $13 billion 335 00:16:40,050 --> 00:16:42,120 and Pepsi ends up making minus-- 336 00:16:42,120 --> 00:16:47,640 I'm sorry, if Coke advertises and Pepsi does not, 337 00:16:47,640 --> 00:16:48,510 they split money. 338 00:16:48,510 --> 00:16:50,700 And Pepsi makes negative 2. 339 00:16:50,700 --> 00:16:52,950 They actually lose money because they have fixed costs 340 00:16:52,950 --> 00:16:53,700 and they don't sell anything. 341 00:16:53,700 --> 00:16:54,500 Nobody buys Pepsi. 342 00:16:54,500 --> 00:16:56,065 It'll lose money. 343 00:16:56,065 --> 00:16:57,440 And let's say if Pepsi advertises 344 00:16:57,440 --> 00:17:00,770 and Coke doesn't, then Coke makes negative 2 345 00:17:00,770 --> 00:17:04,000 and Pepsi makes 13. 346 00:17:04,000 --> 00:17:05,710 So actually, if you don't advertise, 347 00:17:05,710 --> 00:17:07,800 you're really screwed, and the other guy is really screwed. 348 00:17:07,800 --> 00:17:07,980 Yeah? 349 00:17:07,980 --> 00:17:09,930 AUDIENCE: Does this include the cost of advertising? 350 00:17:09,930 --> 00:17:11,347 JONATHAN GRUBER: This does include 351 00:17:11,347 --> 00:17:12,890 the cost of advertising. 352 00:17:12,890 --> 00:17:18,220 But it's just Coke gets a huge market, expands its market. 353 00:17:18,220 --> 00:17:21,220 So now let's play the game. 354 00:17:21,220 --> 00:17:23,170 Well, now let's say you're Coke. 355 00:17:23,170 --> 00:17:30,973 You say, well, if I advertise and Pepsi advertises, I make 3. 356 00:17:30,973 --> 00:17:32,890 But if I don't advertise and Pepsi advertises, 357 00:17:32,890 --> 00:17:33,640 I make negative 2. 358 00:17:33,640 --> 00:17:35,730 So I should advertise. 359 00:17:35,730 --> 00:17:38,700 If I advertise and Pepsi doesn't advertise, I make 13. 360 00:17:38,700 --> 00:17:42,180 If I don't advertise and Pepsi doesn't advertise, I make 8. 361 00:17:42,180 --> 00:17:45,630 So either way, my dominant strategy is to advertise. 362 00:17:45,630 --> 00:17:47,730 And likewise, Pepsi does the same thing. 363 00:17:47,730 --> 00:17:49,110 I screwed up writing this compared to my notes, 364 00:17:49,110 --> 00:17:50,380 but it's good because it shows you-- 365 00:17:50,380 --> 00:17:52,380 I flipped the matrix, but the logic is the same. 366 00:17:52,380 --> 00:17:54,660 It helps you not just memorize cells of the matrix 367 00:17:54,660 --> 00:17:55,980 but learn the logic. 368 00:17:55,980 --> 00:17:58,700 The point is either way, the dominant strategy 369 00:17:58,700 --> 00:18:01,750 is to advertise, so they both advertise. 370 00:18:01,750 --> 00:18:04,430 So real world example of how you can end up. 371 00:18:04,430 --> 00:18:06,470 Now, so much of Pepsi and Coke do this. 372 00:18:06,470 --> 00:18:09,060 Actually, there was an industry that did this. 373 00:18:09,060 --> 00:18:14,870 So when I was a kid, you never, ever saw ads for liquor on TV. 374 00:18:14,870 --> 00:18:18,200 There were beer ads and wine ads, but no hard alcohol ad. 375 00:18:18,200 --> 00:18:21,440 No bourbon, no whiskey, no nothing, gin. 376 00:18:21,440 --> 00:18:23,870 All these Captain Morgan's ads we see now, 377 00:18:23,870 --> 00:18:26,020 they didn't exist when I was a kid. 378 00:18:26,020 --> 00:18:27,520 But it wasn't because the law. 379 00:18:27,520 --> 00:18:30,880 It was because the hard liquor industry cooperatively agreed 380 00:18:30,880 --> 00:18:32,300 none of them would advertise. 381 00:18:32,300 --> 00:18:34,690 So they actually imposed the cooperative equilibrium, 382 00:18:34,690 --> 00:18:35,747 and then that broke down. 383 00:18:35,747 --> 00:18:37,580 I don't know the story of how it broke down. 384 00:18:37,580 --> 00:18:38,180 But it broke down. 385 00:18:38,180 --> 00:18:40,013 Now they all advertise, and they're probably 386 00:18:40,013 --> 00:18:43,360 all worse off than they were when they didn't advertise. 387 00:18:43,360 --> 00:18:45,610 We'll talk next time about why it probably broke down. 388 00:18:45,610 --> 00:18:46,780 I don't know the stories. 389 00:18:46,780 --> 00:18:49,347 I have a rough sense, and we'll talk about that next time. 390 00:18:49,347 --> 00:18:51,930 But this is the point of how a non-cooperative equilibrium can 391 00:18:51,930 --> 00:18:54,840 drive you to a bad outcome. 392 00:18:54,840 --> 00:18:58,260 Now, basically, this doesn't just 393 00:18:58,260 --> 00:18:59,730 apply to prisoners or businesses. 394 00:18:59,730 --> 00:19:01,688 It applies to people, too. 395 00:19:01,688 --> 00:19:03,480 So let's say poor Hector back there has had 396 00:19:03,480 --> 00:19:06,190 a fight with his girlfriend. 397 00:19:06,190 --> 00:19:07,622 And they've had a big fight. 398 00:19:07,622 --> 00:19:08,830 They've going a little while. 399 00:19:08,830 --> 00:19:10,360 They've had a big fight. 400 00:19:10,360 --> 00:19:13,090 And Hector has got to decide, do I apologize or do I wait 401 00:19:13,090 --> 00:19:16,010 for her to apologize? 402 00:19:16,010 --> 00:19:18,770 Well, the last thing Hector wants 403 00:19:18,770 --> 00:19:21,470 is to go up there and apologize and have her say, forget it. 404 00:19:21,470 --> 00:19:22,940 I'm breaking up with you. 405 00:19:22,940 --> 00:19:26,000 That'd be the worst. 406 00:19:26,000 --> 00:19:28,400 If he knows she's going to be like, oh, I'm sorry, too, 407 00:19:28,400 --> 00:19:29,850 then he'd be happy to do it. 408 00:19:29,850 --> 00:19:31,940 But what if he goes, no I'm breaking up with you, 409 00:19:31,940 --> 00:19:33,720 and she's thinking the same thing. 410 00:19:33,720 --> 00:19:36,580 So what happens, they break up. 411 00:19:36,580 --> 00:19:38,900 We've been through this many times in our lives. 412 00:19:38,900 --> 00:19:42,060 This is the non-cooperative strategy. 413 00:19:42,060 --> 00:19:44,560 Basically, if you know what the other person is going to do, 414 00:19:44,560 --> 00:19:48,970 your dominant strategies to be an asshole, and basically that 415 00:19:48,970 --> 00:19:53,720 happens a lot in the context of the real world. 416 00:19:53,720 --> 00:19:58,280 So now we have this sad-sounding outcome, 417 00:19:58,280 --> 00:20:01,700 that basically game theory leads to bad outcomes for producers, 418 00:20:01,700 --> 00:20:03,060 at least. 419 00:20:03,060 --> 00:20:05,470 But this is what's exciting about game theory. 420 00:20:05,470 --> 00:20:07,380 So when I went to grad school, back 421 00:20:07,380 --> 00:20:10,530 when dinosaurs roamed the earth, game theory 422 00:20:10,530 --> 00:20:12,980 was taught barely in the sequence. 423 00:20:12,980 --> 00:20:15,270 It was like an extra course, taught a little bit. 424 00:20:15,270 --> 00:20:19,400 Now it dominates the teaching of microeconomics, in economics. 425 00:20:19,400 --> 00:20:22,380 And it doesn't dominate, but it's a whole like component 426 00:20:22,380 --> 00:20:24,750 of our core microeconomics education, 427 00:20:24,750 --> 00:20:27,510 because it's given such a cool set of tools 428 00:20:27,510 --> 00:20:29,040 to think about these decisions. 429 00:20:29,040 --> 00:20:33,090 Now, I can't give you even 1% of the flavor of game theory. 430 00:20:33,090 --> 00:20:35,910 If you want to learn more, I highly suggest you take 1412, 431 00:20:35,910 --> 00:20:38,190 which our game theory class, and you can learn a ton. 432 00:20:38,190 --> 00:20:39,982 But let me show you one interesting wrinkle 433 00:20:39,982 --> 00:20:43,590 of the things game theory can do, to go beyond this. 434 00:20:43,590 --> 00:20:48,690 And that's to imagine that Coke and Pepsi are not playing a one 435 00:20:48,690 --> 00:20:50,980 shot game, but a repeated game. 436 00:20:56,050 --> 00:20:59,110 Repeated game. 437 00:20:59,110 --> 00:21:07,250 So now imagine that Coke says to Pepsi the following, 438 00:21:07,250 --> 00:21:13,440 I promise to not advertise as long as you don't advertise. 439 00:21:13,440 --> 00:21:18,245 But if you ever advertise, I will advertise forever. 440 00:21:18,245 --> 00:21:19,620 Coke says to Pepsi, I promise not 441 00:21:19,620 --> 00:21:21,390 to advertise as long as you don't advertise, 442 00:21:21,390 --> 00:21:22,930 but if I ever catch you advertising, 443 00:21:22,930 --> 00:21:25,770 I'm going to advertise forever. 444 00:21:25,770 --> 00:21:29,610 So think about Pepsi choice in period 1. 445 00:21:29,610 --> 00:21:31,050 Pepsi's choice in period 1. 446 00:21:31,050 --> 00:21:33,972 In period 1, they could say, ha, stupid Coke. 447 00:21:33,972 --> 00:21:35,430 I'm going to jump on and advertise. 448 00:21:35,430 --> 00:21:37,380 They promised not to advertise. 449 00:21:37,380 --> 00:21:45,440 So if Pepsi advertises, they're going to make 13 in period 1 450 00:21:45,440 --> 00:21:48,200 because Coke's taken themselves off to the side. 451 00:21:48,200 --> 00:21:54,857 But after period 1, they're going to make 8 forever. 452 00:21:54,857 --> 00:21:55,440 No, I'm sorry. 453 00:21:55,440 --> 00:21:56,720 They're going to make 3 forever. 454 00:21:56,720 --> 00:21:57,860 Because Coke's going to advertise. 455 00:21:57,860 --> 00:21:58,985 They're going to advertise. 456 00:21:58,985 --> 00:22:03,177 They break down to the non-cooperative equilibrium, 457 00:22:03,177 --> 00:22:04,010 if Pepsi advertises. 458 00:22:04,010 --> 00:22:06,710 Now, what if Pepsi doesn't advertise? 459 00:22:06,710 --> 00:22:09,590 As long as it doesn't advertise, then it gets to deal with Coke, 460 00:22:09,590 --> 00:22:10,850 so it makes 8 forever. 461 00:22:14,570 --> 00:22:17,495 We'll talk later in the course about how you combine numbers 462 00:22:17,495 --> 00:22:19,370 that happen at different times, but trust me, 463 00:22:19,370 --> 00:22:23,390 8 forever is a way better deal than 13, than 3 forever. 464 00:22:23,390 --> 00:22:27,810 So actually, by having this be a repeated game, 465 00:22:27,810 --> 00:22:31,730 Coke has solved the prisoner's dilemma. 466 00:22:31,730 --> 00:22:34,790 It's essentially imposed a cooperative equilibrium 467 00:22:34,790 --> 00:22:37,490 on the problem. 468 00:22:37,490 --> 00:22:39,950 So that's how repeated game can fix this. 469 00:22:39,950 --> 00:22:42,890 But-- this is where the game gets really exciting-- that 470 00:22:42,890 --> 00:22:46,570 only works if this game never ends, 471 00:22:46,570 --> 00:22:48,610 because once Coke or Pepsi thinks 472 00:22:48,610 --> 00:22:53,510 there's an end to the game, the entire thing breaks down. 473 00:22:53,510 --> 00:22:56,630 So imagine, for example, that Coke makes the offer to Pepsi, 474 00:22:56,630 --> 00:22:58,310 but Pepsi is worried that in 10 years, 475 00:22:58,310 --> 00:23:01,007 the government is going to outlaw soda. 476 00:23:01,007 --> 00:23:03,340 The government said, look, we're heading that direction. 477 00:23:03,340 --> 00:23:05,635 Soda is going to be illegal in 10 years, 478 00:23:05,635 --> 00:23:06,760 so I don't want to do this. 479 00:23:09,570 --> 00:23:11,500 I'm sorry, I have that in my mind. 480 00:23:11,500 --> 00:23:14,230 So Coke offers the deal now, what do I think? 481 00:23:14,230 --> 00:23:19,000 Well, let's think about Pepsi's decision in the ninth year. 482 00:23:19,000 --> 00:23:22,900 They've made 8, 8, 8, 8, 8, and they get to year 9. 483 00:23:22,900 --> 00:23:28,110 Now in year 9, they know that next year there's no more game. 484 00:23:28,110 --> 00:23:30,370 So what should they do? 485 00:23:30,370 --> 00:23:30,970 Advertise. 486 00:23:30,970 --> 00:23:34,750 Grab the 13 in the last period, because Coke can't punish them 487 00:23:34,750 --> 00:23:37,360 because the game's over. 488 00:23:37,360 --> 00:23:39,670 But Coke knows this. 489 00:23:39,670 --> 00:23:41,950 So what's Coke going to do in the ninth year? 490 00:23:41,950 --> 00:23:42,860 Advertise. 491 00:23:42,860 --> 00:23:48,000 It's going to advertise, so they're both going to make 3. 492 00:23:48,000 --> 00:23:49,465 Well, if Pepsi knows Coke's going 493 00:23:49,465 --> 00:23:51,550 to advertise in the ninth year no matter what, 494 00:23:51,550 --> 00:23:53,640 what should Pepsi in the eighth year? 495 00:23:53,640 --> 00:23:54,475 Advertise. 496 00:23:54,475 --> 00:23:56,350 And if Coke knows Pepsi is going to advertise 497 00:23:56,350 --> 00:23:58,017 in the eighth year, what should Coke do? 498 00:23:58,017 --> 00:24:00,750 And so on, and it ends up that they both advertise all the way 499 00:24:00,750 --> 00:24:02,480 through. 500 00:24:02,480 --> 00:24:04,430 So the game breaks down if it's an end. 501 00:24:04,430 --> 00:24:06,535 This is really kind of neat, and this 502 00:24:06,535 --> 00:24:07,910 is what game theory is all about, 503 00:24:07,910 --> 00:24:09,350 is how do you think through these more 504 00:24:09,350 --> 00:24:11,210 complicated scenarios that are much more complicated 505 00:24:11,210 --> 00:24:12,680 than the prisoner's dilemma, and actually 506 00:24:12,680 --> 00:24:14,360 think about how firms and individuals might actually 507 00:24:14,360 --> 00:24:14,860 behave? 508 00:24:14,860 --> 00:24:15,904 Yeah? 509 00:24:15,904 --> 00:24:18,196 AUDIENCE: Wouldn't it also be advantageous if they just 510 00:24:18,196 --> 00:24:20,780 advertised the first year instead of these contracts, 511 00:24:20,780 --> 00:24:23,010 kind of what we were talking about earlier? 512 00:24:23,010 --> 00:24:24,100 JONATHAN GRUBER: Sure. 513 00:24:24,100 --> 00:24:26,380 And once again, that's what you cover in a field 514 00:24:26,380 --> 00:24:27,380 course like game theory. 515 00:24:27,380 --> 00:24:29,382 What about alternative forms of contracting, 516 00:24:29,382 --> 00:24:30,840 with exclusionary contracting, what 517 00:24:30,840 --> 00:24:32,952 we call tying in contracting? 518 00:24:32,952 --> 00:24:34,160 That's great, and they would. 519 00:24:34,160 --> 00:24:36,890 But that's why you got to take 1412, OK? 520 00:24:36,890 --> 00:24:37,390 Yeah? 521 00:24:39,927 --> 00:24:41,510 AUDIENCE: Would it be a better outcome 522 00:24:41,510 --> 00:24:45,845 if they cooperated and switched periods of advertising? 523 00:24:45,845 --> 00:24:49,022 Like for the first period, they get 13, they get minus 2. 524 00:24:49,022 --> 00:24:50,480 JONATHAN GRUBER: Yeah, the way I've 525 00:24:50,480 --> 00:24:52,188 set this problem up, if they could commit 526 00:24:52,188 --> 00:24:54,050 to that, that would be right. 527 00:24:54,050 --> 00:24:55,670 But you'd have to commit to it. 528 00:24:55,670 --> 00:24:59,090 Because then the period that Pepsi promised to take off, 529 00:24:59,090 --> 00:25:01,700 if they actually advertised that period, then Coke's screwed. 530 00:25:01,700 --> 00:25:04,730 So that would work as a repeated game solution, 531 00:25:04,730 --> 00:25:08,230 but it wouldn't work as a non-repeating game. 532 00:25:08,230 --> 00:25:10,760 It would work as an infinite repeated game but not 533 00:25:10,760 --> 00:25:13,290 a non-infinite repeated game. 534 00:25:13,290 --> 00:25:14,255 Good question. 535 00:25:14,255 --> 00:25:16,310 OK, other questions? 536 00:25:16,310 --> 00:25:18,367 All right, so that's the basis of game theory. 537 00:25:18,367 --> 00:25:19,950 That's just a taste for the excitement 538 00:25:19,950 --> 00:25:21,500 that you can learn with game theory. 539 00:25:21,500 --> 00:25:23,105 But in fact, in economics, we like 540 00:25:23,105 --> 00:25:24,980 to write those as fun examples, but we really 541 00:25:24,980 --> 00:25:26,457 prefer to do math. 542 00:25:26,457 --> 00:25:28,040 So let's actually think about the math 543 00:25:28,040 --> 00:25:29,510 of how we take game theory concepts 544 00:25:29,510 --> 00:25:31,040 and put them in practice. 545 00:25:31,040 --> 00:25:34,880 And the way we do that is through the concept 546 00:25:34,880 --> 00:25:35,960 of the Cournot model. 547 00:25:39,720 --> 00:25:42,550 The Cournot model of non-cooperative oligopolies. 548 00:25:46,500 --> 00:25:48,957 So the Cournot model of non-cooperative oligopoly 549 00:25:48,957 --> 00:25:50,290 is the standard workhorse model. 550 00:25:50,290 --> 00:25:52,720 It takes this intuition and puts it 551 00:25:52,720 --> 00:25:54,340 into the optimizing math we've been 552 00:25:54,340 --> 00:25:55,630 doing so far in this class. 553 00:25:58,510 --> 00:26:01,030 Now let's imagine non-cooperative case, 554 00:26:01,030 --> 00:26:02,907 but now let's imagine not just two choices, 555 00:26:02,907 --> 00:26:04,990 but realistically, there's a whole set of choices. 556 00:26:08,290 --> 00:26:13,010 Then how would you behave in that case? 557 00:26:13,010 --> 00:26:16,240 So let's imagine that there's two airlines, United 558 00:26:16,240 --> 00:26:18,930 and American. 559 00:26:18,930 --> 00:26:23,370 So we have an oligopolistic two-firm airline industry. 560 00:26:23,370 --> 00:26:25,380 Obviously, the math can extend to more firms, 561 00:26:25,380 --> 00:26:28,180 but just to start, and I'll talk about that next lecture. 562 00:26:28,180 --> 00:26:30,780 But for now, imagine a two-firm industry, United and American. 563 00:26:30,780 --> 00:26:32,280 And because the hub and spoke system 564 00:26:32,280 --> 00:26:34,200 we discussed last time, let's imagine 565 00:26:34,200 --> 00:26:37,380 that they're the only two folks that go from Boston to Chicago. 566 00:26:37,380 --> 00:26:38,910 Because it's hub and spoke system. 567 00:26:38,910 --> 00:26:40,260 The only folks that go from Boston to Chicago 568 00:26:40,260 --> 00:26:41,640 are United and American, and they do, in fact, 569 00:26:41,640 --> 00:26:42,930 dominate that line. 570 00:26:42,930 --> 00:26:45,200 So let's imagine they're the only folks, 571 00:26:45,200 --> 00:26:47,880 and say no other firms can compete on this route 572 00:26:47,880 --> 00:26:50,250 because they can't get slots at the airport. 573 00:26:50,250 --> 00:26:52,310 So the question is, how do these firms 574 00:26:52,310 --> 00:26:54,450 decide how many flights to run? 575 00:26:54,450 --> 00:26:56,420 It's not just advertise, don't. 576 00:26:56,420 --> 00:26:58,400 It's literally a continuous decision 577 00:26:58,400 --> 00:27:03,480 of how many flights to run every day and how much to charge. 578 00:27:03,480 --> 00:27:05,650 They've got to make that decision. 579 00:27:05,650 --> 00:27:11,970 And the Nash equilibrium here, the subset of Nash, 580 00:27:11,970 --> 00:27:14,790 for this example, is called the Cournot equilibrium. 581 00:27:14,790 --> 00:27:18,010 And the Cournot equilibrium exists 582 00:27:18,010 --> 00:27:22,380 when a firm chooses a quantity such 583 00:27:22,380 --> 00:27:25,770 that, given the quantity chosen by the other firm, 584 00:27:25,770 --> 00:27:28,000 they don't want to change. 585 00:27:28,000 --> 00:27:31,410 So a firm chooses, essentially, a profit-maximizing quantity, 586 00:27:31,410 --> 00:27:35,640 given the quantity chosen by the other firm. 587 00:27:35,640 --> 00:27:41,640 And that profit-maximizing quantity, then you're 588 00:27:41,640 --> 00:27:43,530 in Cournot equilibrium, if you have 589 00:27:43,530 --> 00:27:48,000 chosen a quantity that is profit-maximizing, given 590 00:27:48,000 --> 00:27:51,000 what the other firm is doing. 591 00:27:51,000 --> 00:27:54,120 So basically, how do we actually carry this out? 592 00:27:54,120 --> 00:27:57,480 Let's talk about the steps. 593 00:27:57,480 --> 00:28:01,415 So the first step, I'm going to talk intuitively 594 00:28:01,415 --> 00:28:03,040 about the math, what we're going to do, 595 00:28:03,040 --> 00:28:03,900 and then I'm going to talk mathematically 596 00:28:03,900 --> 00:28:05,710 and graph what we actually do. 597 00:28:05,710 --> 00:28:08,580 There's essentially three steps in solving for the Cournot 598 00:28:08,580 --> 00:28:10,200 equilibrium. 599 00:28:10,200 --> 00:28:15,270 The first is ask how your demand changes when some of it's 600 00:28:15,270 --> 00:28:16,540 absorbed by other firms. 601 00:28:16,540 --> 00:28:21,320 So the first is solve for your residual demand function. 602 00:28:21,320 --> 00:28:22,940 What does your demand curve look like, 603 00:28:22,940 --> 00:28:25,630 given what the other firm does? 604 00:28:25,630 --> 00:28:28,010 That's step 1. 605 00:28:28,010 --> 00:28:32,450 Step 2 is then you develop a marginal revenue, which 606 00:28:32,450 --> 00:28:37,930 is a function of the other firm's quantity. 607 00:28:37,930 --> 00:28:38,750 Little q. 608 00:28:38,750 --> 00:28:41,103 It's multiple firms. 609 00:28:41,103 --> 00:28:43,270 The other firm's-- that's really bad, hard to read-- 610 00:28:43,270 --> 00:28:44,312 the other firm's quality. 611 00:28:44,312 --> 00:28:46,030 So your marginal revenue is a function. 612 00:28:46,030 --> 00:28:47,290 Typically, it's a function-- 613 00:28:47,290 --> 00:28:49,540 I'm sorry-- of both your quantity and the other firm's 614 00:28:49,540 --> 00:28:50,740 quantity. 615 00:28:50,740 --> 00:28:53,485 A function of both your quantity and the other firm's quantity. 616 00:28:53,485 --> 00:28:56,110 We develop marginal revenue as a function of your own quantity. 617 00:28:56,110 --> 00:28:57,190 We know how to do that. 618 00:28:57,190 --> 00:28:59,440 Now we develop a margin as a function of your quantity 619 00:28:59,440 --> 00:29:02,010 and the other firm's quantity. 620 00:29:02,010 --> 00:29:04,800 Then you simply set this marginal revenue 621 00:29:04,800 --> 00:29:07,980 equal to marginal cost, and that delivers 622 00:29:07,980 --> 00:29:10,200 you a conditional answer. 623 00:29:10,200 --> 00:29:14,670 That delivers you your optimal quantity as a function 624 00:29:14,670 --> 00:29:16,170 of the other firm's quantity. 625 00:29:19,805 --> 00:29:21,680 Well, that doesn't do us a whole lot of good, 626 00:29:21,680 --> 00:29:24,680 except there's two firms. 627 00:29:24,680 --> 00:29:32,170 So the fourth step is we do the same thing for the other firm 628 00:29:32,170 --> 00:29:34,330 and get the same kind of equation. 629 00:29:34,330 --> 00:29:35,620 Then what do we have? 630 00:29:35,620 --> 00:29:37,840 Two equations and two unknowns, so we solve. 631 00:29:43,790 --> 00:29:45,440 So what we do here is essentially 632 00:29:45,440 --> 00:29:48,230 the same thing we did before, but now your marginal revenue 633 00:29:48,230 --> 00:29:49,650 is not just a function of your own quantity, 634 00:29:49,650 --> 00:29:51,200 it's a function of the other guy's quantity. 635 00:29:51,200 --> 00:29:52,430 Same with the other guy. 636 00:29:52,430 --> 00:29:54,222 That gives you two equations, two unknowns. 637 00:29:54,222 --> 00:29:54,740 We solve. 638 00:29:54,740 --> 00:29:57,560 And the point at which both firms are happy 639 00:29:57,560 --> 00:29:59,562 is the Cournot equilibrium. 640 00:30:02,400 --> 00:30:05,807 That's confusing, so let's actually look at that. 641 00:30:05,807 --> 00:30:07,890 We'll do this both graphically and mathematically. 642 00:30:07,890 --> 00:30:11,390 Let's start with figure 13.1. 643 00:30:11,390 --> 00:30:15,260 To make things easy, let's start by imagining that American 644 00:30:15,260 --> 00:30:17,390 Airlines is a monopoly. 645 00:30:17,390 --> 00:30:22,870 Let's start with the world with an American Airlines monopoly. 646 00:30:22,870 --> 00:30:30,250 And let's say that the demand function is P equals 339 647 00:30:30,250 --> 00:30:35,555 minus Q. That's the demand for flights from Boston to Chicago. 648 00:30:40,050 --> 00:30:43,842 And let's say that the marginal cost, to make life easier-- 649 00:30:43,842 --> 00:30:46,300 it could have a cost function and make your life difficult, 650 00:30:46,300 --> 00:30:47,890 and maybe someday I'll do that. 651 00:30:47,890 --> 00:30:49,390 But for now, to make your life easy, 652 00:30:49,390 --> 00:30:54,418 let's just say it's a flat marginal cost of $147. 653 00:30:54,418 --> 00:30:56,460 I'm not going to make life difficult with solving 654 00:30:56,460 --> 00:30:57,840 for marginal cost functions. 655 00:30:57,840 --> 00:31:00,180 For now, it's just a flat marginal cost of $147. 656 00:31:00,180 --> 00:31:05,290 No matter how many flights they do, it's $147 per passenger. 657 00:31:05,290 --> 00:31:09,640 So if you're a monopolist, how do you solve this problem? 658 00:31:09,640 --> 00:31:12,805 Well, first you derive your marginal revenue function. 659 00:31:12,805 --> 00:31:14,430 Well, what's marginal revenue function? 660 00:31:14,430 --> 00:31:21,840 Well, revenues is P times Q, which is 339 minus q squared. 661 00:31:21,840 --> 00:31:27,607 So your marginal revenue function is 339 minus 2Q. 662 00:31:27,607 --> 00:31:29,190 That's your marginal revenue function, 663 00:31:29,190 --> 00:31:30,840 if you're the monopolist. 664 00:31:30,840 --> 00:31:32,380 What's your marginal cost? 665 00:31:32,380 --> 00:31:36,930 Well, I just said it's $147. 666 00:31:36,930 --> 00:31:38,550 And then you just solve. 667 00:31:38,550 --> 00:31:43,650 And when you solve that, you get that Q, the optimal quantity, 668 00:31:43,650 --> 00:31:47,620 is 96 flights. 669 00:31:47,620 --> 00:31:50,685 And then how do you get the price? 670 00:31:50,685 --> 00:31:52,560 How do you get the price of monopoly problem? 671 00:31:52,560 --> 00:31:54,900 How do we know what the price is? 672 00:31:54,900 --> 00:31:55,615 Yeah? 673 00:31:55,615 --> 00:31:57,990 AUDIENCE: Where the quantity intersects the demand curve. 674 00:31:57,990 --> 00:31:59,120 JONATHAN GRUBER: You've got to plug it back 675 00:31:59,120 --> 00:32:00,238 into the demand curve. 676 00:32:00,238 --> 00:32:02,530 Take that quantity, plug it back into the demand curve. 677 00:32:02,530 --> 00:32:10,860 So the price is 339 minus 96, or 243. 678 00:32:10,860 --> 00:32:15,000 So I just solved the monopoly problem quickly, 679 00:32:15,000 --> 00:32:18,000 but that's what we've done already in this class. 680 00:32:18,000 --> 00:32:20,110 And you could see that in the graph here. 681 00:32:20,110 --> 00:32:22,840 In figure 13.1, you've got demand curve, 682 00:32:22,840 --> 00:32:26,160 which is P equals 339 minus Q. You've 683 00:32:26,160 --> 00:32:30,050 got a supply curve, which is the flat marginal cost of $147. 684 00:32:30,050 --> 00:32:33,030 You develop a marginal revenue function, 685 00:32:33,030 --> 00:32:36,733 which is 339 minus 2Q. 686 00:32:36,733 --> 00:32:38,150 As in our previous example, that's 687 00:32:38,150 --> 00:32:41,210 just basically an inward shift of the demand function. 688 00:32:41,210 --> 00:32:46,090 That intersects marginal costs at 96 flights. 689 00:32:46,090 --> 00:32:48,250 We have 1,000 passengers per quarter. 690 00:32:48,250 --> 00:32:50,980 It doesn't really matter. 691 00:32:50,980 --> 00:32:53,850 It's just all standardization. 692 00:32:53,850 --> 00:32:56,350 And then to get the price, you read it off the demand curve. 693 00:32:56,350 --> 00:33:00,120 You say 96 flights means the price of $243 per flight. 694 00:33:00,120 --> 00:33:06,130 OK, that's what we do if American was a monopolist. 695 00:33:06,130 --> 00:33:09,580 Now, however, American is not a monopolist. 696 00:33:09,580 --> 00:33:12,400 American deals with United, and American doesn't know 697 00:33:12,400 --> 00:33:14,890 what United is going to do. 698 00:33:14,890 --> 00:33:16,750 So what does American do? 699 00:33:16,750 --> 00:33:21,630 Well, let's say American has to deal with the fact-- 700 00:33:21,630 --> 00:33:24,850 it now has to recognize that it's got its own demand 701 00:33:24,850 --> 00:33:28,900 function, qa, which is the total quantity 702 00:33:28,900 --> 00:33:32,770 in the market minus qu. 703 00:33:32,770 --> 00:33:36,200 So it has a residual demand function, 704 00:33:36,200 --> 00:33:41,380 which is the total demand in the market minus what United sells. 705 00:33:41,380 --> 00:33:44,920 So suppose, for example, American thinks-- 706 00:33:44,920 --> 00:33:47,400 American's got a spy inside United-- 707 00:33:47,400 --> 00:33:49,500 and American says, ha, I think United 708 00:33:49,500 --> 00:33:53,382 is going to fly 64 flights. 709 00:33:53,382 --> 00:33:54,840 So imagine American thinks United's 710 00:33:54,840 --> 00:33:59,550 going to fly 64 flights. 711 00:33:59,550 --> 00:34:05,250 Well, in that case, if they're going to fly 64 flights, 712 00:34:05,250 --> 00:34:12,159 then my demand function is p sub a equals 339 minus q 713 00:34:12,159 --> 00:34:19,320 sub a minus 64, because the big quantity 714 00:34:19,320 --> 00:34:23,670 is little qa plus little qu. 715 00:34:23,670 --> 00:34:30,520 So my demand function is 339 minus q sub a minus 64. 716 00:34:30,520 --> 00:34:34,239 Or in other words, my residual demand function 717 00:34:34,239 --> 00:34:46,090 is that p sub a equals 339 equals 275 minus qa. 718 00:34:46,090 --> 00:34:49,480 So if I think United's going to fly 64 flights, 719 00:34:49,480 --> 00:34:54,670 then my effective demand function is 275 minus q. 720 00:34:54,670 --> 00:34:56,260 And then I'm done. 721 00:34:56,260 --> 00:34:58,990 Then I just solve for, what would I do as a monopolist, 722 00:34:58,990 --> 00:35:01,600 given the other guy's flying 64 flights? 723 00:35:01,600 --> 00:35:06,560 So you can see that in figure 13.2. 724 00:35:06,560 --> 00:35:09,260 So I have a demand function. 725 00:35:09,260 --> 00:35:12,050 I say, well, if United's going to fly 64 flights, that demand 726 00:35:12,050 --> 00:35:14,882 function gets shifted in by 64. 727 00:35:14,882 --> 00:35:17,090 And then I'm going to do the same thing I did before. 728 00:35:17,090 --> 00:35:19,396 I solve for marginal revenue. 729 00:35:19,396 --> 00:35:21,490 I'm going to solve for marginal revenue 730 00:35:21,490 --> 00:35:23,210 and I intersect that with marginal cost. 731 00:35:23,210 --> 00:35:28,480 That's going to happen at 64 flights and a price of $211. 732 00:35:28,480 --> 00:35:30,738 So basically, it's the same exercise. 733 00:35:30,738 --> 00:35:31,530 It's not that hard. 734 00:35:31,530 --> 00:35:34,380 You just first take out what United is going to do. 735 00:35:34,380 --> 00:35:37,330 The problem is American doesn't have a spy. 736 00:35:37,330 --> 00:35:40,060 They don't really know what United's going to do. 737 00:35:40,060 --> 00:35:42,370 They have to essentially develop a strategy, 738 00:35:42,370 --> 00:35:46,060 given the possibilities of what United might do. 739 00:35:46,060 --> 00:35:49,420 They have to say, look, I don't know what q sub u is, 740 00:35:49,420 --> 00:35:54,940 so I have to devise my optimal strategy given q sub u. 741 00:35:54,940 --> 00:35:57,790 In other words, I have to simultaneously solve 742 00:35:57,790 --> 00:36:01,540 for what I would do at every possible quantity United 743 00:36:01,540 --> 00:36:03,890 would sell. 744 00:36:03,890 --> 00:36:06,810 I have to solve what I would do for every possible quantity 745 00:36:06,810 --> 00:36:07,560 United would sell. 746 00:36:07,560 --> 00:36:12,180 And we call this developing your reaction, 747 00:36:12,180 --> 00:36:13,770 or best response curve. 748 00:36:17,300 --> 00:36:20,840 Your reaction curve or your best response curve, 749 00:36:20,840 --> 00:36:23,500 which is, what is the best thing to do, given 750 00:36:23,500 --> 00:36:25,372 what the other guy's doing? 751 00:36:25,372 --> 00:36:26,830 What is the best thing to do, given 752 00:36:26,830 --> 00:36:28,770 what the other guys doing? 753 00:36:28,770 --> 00:36:34,030 You could see that in figure 13.3, we show how that works. 754 00:36:34,030 --> 00:36:36,320 That shows best response curves. 755 00:36:36,320 --> 00:36:41,740 So for example, look at the intersection on the y-axis, 756 00:36:41,740 --> 00:36:45,160 where the red line hits the y-axis. 757 00:36:45,160 --> 00:36:47,020 That was our monopoly equilibrium. 758 00:36:50,980 --> 00:36:53,710 I'm sorry, where the blue line hits the x-axis, my bad. 759 00:36:53,710 --> 00:36:54,760 We're doing American. 760 00:36:54,760 --> 00:36:57,670 Look at where the blue line hits the x-axis. 761 00:36:57,670 --> 00:37:00,970 That is assuming zero United flights. 762 00:37:00,970 --> 00:37:02,650 Where the blue line is the x-axis 763 00:37:02,650 --> 00:37:04,210 is where there's zero United flights. 764 00:37:04,210 --> 00:37:07,260 Well, we know what American would do there. 765 00:37:07,260 --> 00:37:09,720 They would fly 96 flights. 766 00:37:09,720 --> 00:37:11,760 We already solved that. 767 00:37:11,760 --> 00:37:18,370 Now look at the point where United is flying 64 flights. 768 00:37:18,370 --> 00:37:22,752 Well, we also know what American would do then. 769 00:37:22,752 --> 00:37:24,710 We know that we solved, in the previous figure, 770 00:37:24,710 --> 00:37:27,130 they would then do 64 flights. 771 00:37:27,130 --> 00:37:31,540 And in general, what that blue line is is for every quantity 772 00:37:31,540 --> 00:37:34,642 that United flies, what does American want to fly? 773 00:37:40,470 --> 00:37:44,640 So meanwhile, United is doing the same mathematics. 774 00:37:44,640 --> 00:37:47,250 Imagine, to make life easier-- we'll almost always do this 775 00:37:47,250 --> 00:37:48,360 to make life easy-- 776 00:37:48,360 --> 00:37:52,830 imagine United has the same marginal costs as American, 777 00:37:52,830 --> 00:37:56,440 and obviously faces the same market demand curve. 778 00:37:56,440 --> 00:37:59,670 Well then, literally, their math is totally symmetric. 779 00:37:59,670 --> 00:38:01,860 If American wasn't in the market, 780 00:38:01,860 --> 00:38:04,920 you'd have where the red line intersects the vertical axis. 781 00:38:04,920 --> 00:38:06,720 If American was flying zero, United 782 00:38:06,720 --> 00:38:09,390 would flight 96 flights, because their problem 783 00:38:09,390 --> 00:38:13,140 is identical to American's monopoly problem. 784 00:38:13,140 --> 00:38:17,920 So the red line is United's best response curve. 785 00:38:17,920 --> 00:38:20,470 So we've graphed, for every possible amount 786 00:38:20,470 --> 00:38:22,420 of flights that United does, what's 787 00:38:22,420 --> 00:38:24,803 American's optimal amount of flights. 788 00:38:24,803 --> 00:38:26,470 We've solved for every amount of flights 789 00:38:26,470 --> 00:38:29,140 that American does with United's also amount of flights. 790 00:38:29,140 --> 00:38:34,320 Where those lines intersect is the Cournot equilibrium. 791 00:38:34,320 --> 00:38:35,820 Why is that the Cournot equilibrium? 792 00:38:35,820 --> 00:38:38,520 Because at that point, both firms 793 00:38:38,520 --> 00:38:40,800 are doing the best they can, given 794 00:38:40,800 --> 00:38:42,790 what the other firm's chosen. 795 00:38:42,790 --> 00:38:44,760 Or in other words, to say this is 796 00:38:44,760 --> 00:38:46,770 given what the other firm's doing, 797 00:38:46,770 --> 00:38:49,080 neither firm wants to deviate. 798 00:38:49,080 --> 00:38:53,077 The profit-maximizing choice is to be where they are, given 799 00:38:53,077 --> 00:38:54,160 the other firm's behavior. 800 00:38:57,420 --> 00:38:59,760 So basically, the Cournot equilibrium 801 00:38:59,760 --> 00:39:03,943 is the only equilibrium that's possible in this market. 802 00:39:03,943 --> 00:39:04,610 And why is that? 803 00:39:04,610 --> 00:39:08,170 So for example, imagine that American came in and said, 804 00:39:08,170 --> 00:39:10,407 look, I like doing 96 flights. 805 00:39:10,407 --> 00:39:11,490 I love being a monopolist. 806 00:39:11,490 --> 00:39:13,800 I'm just going to do 96 flights. 807 00:39:13,800 --> 00:39:18,210 I'm going to do 96 flights, I'm going to charge $243. 808 00:39:18,210 --> 00:39:20,280 Well, in that case, American-- 809 00:39:20,280 --> 00:39:26,800 United, I'm sorry-- would happily come in at $242 810 00:39:26,800 --> 00:39:29,440 and undercut them and sell lots of flights, 811 00:39:29,440 --> 00:39:32,330 because that's still well above marginal cost. 812 00:39:32,330 --> 00:39:37,190 So that's not an equilibrium because United and American are 813 00:39:37,190 --> 00:39:38,690 choosing different outcomes. 814 00:39:38,690 --> 00:39:41,390 It's only equilibrium if they're both to the point 815 00:39:41,390 --> 00:39:45,010 where the same outcome makes them both happy. 816 00:39:45,010 --> 00:39:47,290 So that's the graphics. 817 00:39:47,290 --> 00:39:48,577 Let's do the math here. 818 00:39:48,577 --> 00:39:49,660 Let's do the Cournot math. 819 00:39:53,970 --> 00:39:58,470 In general, the residual demand for American 820 00:39:58,470 --> 00:40:07,020 is that p equals 339 minus qa minus qu. 821 00:40:07,020 --> 00:40:08,760 Remember, big Q is qa plus qu. 822 00:40:11,300 --> 00:40:16,590 Since the demand function is 339 minus big Q, 823 00:40:16,590 --> 00:40:19,296 I simply broke big Q into qa and qu. 824 00:40:19,296 --> 00:40:22,080 Stop me if this is all unclear. 825 00:40:22,080 --> 00:40:25,620 Simply broke the big Q into those two components. 826 00:40:25,620 --> 00:40:28,615 So that means that American's revenue function-- 827 00:40:28,615 --> 00:40:32,100 it's called revenue A, revenue for American-- 828 00:40:32,100 --> 00:40:40,920 is 339 times qa minus qa squared minus qaqu. 829 00:40:40,920 --> 00:40:42,965 This is a new term. 830 00:40:42,965 --> 00:40:44,340 This was the old revenue function 831 00:40:44,340 --> 00:40:45,757 we had when they were monopolists. 832 00:40:45,757 --> 00:40:49,730 Now we've got this new term that didn't exist before. 833 00:40:49,730 --> 00:40:53,600 So that means the marginal revenue for American 834 00:40:53,600 --> 00:40:57,980 is now 339 minus 2qa minus qu. 835 00:41:00,960 --> 00:41:03,720 So now their marginal revenue is actually 836 00:41:03,720 --> 00:41:05,670 a function now of their own behavior, 837 00:41:05,670 --> 00:41:08,220 but their competitor's behavior. 838 00:41:08,220 --> 00:41:12,090 That's the new margin revenue function. 839 00:41:12,090 --> 00:41:14,770 But the profit maximization rule is the same. 840 00:41:14,770 --> 00:41:16,840 We just set that equal to marginal cost. 841 00:41:16,840 --> 00:41:20,430 We set it equal to 147, and you solve. 842 00:41:20,430 --> 00:41:24,180 And what you end up getting is that q sub a star-- 843 00:41:24,180 --> 00:41:36,160 the outcome of q sub a is 96 minus 1/2qu star, or qu. 844 00:41:36,160 --> 00:41:38,950 qa star is 96 minus 1/2qu. 845 00:41:38,950 --> 00:41:41,350 If you solve this equation, that's what you get. 846 00:41:41,350 --> 00:41:45,390 That's 1/2, 1/2 qu. 847 00:41:45,390 --> 00:41:47,850 So now we have the optimal quantity, 848 00:41:47,850 --> 00:41:50,960 but it's a function of what the other guy does. 849 00:41:50,960 --> 00:41:54,400 That's a problem, except that we use the same math for United. 850 00:41:54,400 --> 00:41:56,347 Now, if the problem's symmetric, you 851 00:41:56,347 --> 00:41:57,680 don't have to do the math again. 852 00:41:57,680 --> 00:41:59,930 You know the best response function will be symmetric, 853 00:41:59,930 --> 00:42:01,620 but that won't always be the case. 854 00:42:01,620 --> 00:42:03,380 So I'm going to shortcut here of saying 855 00:42:03,380 --> 00:42:07,250 the best response function for qu 856 00:42:07,250 --> 00:42:11,920 is q star u equals 96 minus 1/2qa. 857 00:42:14,732 --> 00:42:16,940 So I've just written down the best response function. 858 00:42:16,940 --> 00:42:18,610 This corresponds to the graph. 859 00:42:18,610 --> 00:42:23,360 So q star a, that's the blue line. 860 00:42:23,360 --> 00:42:24,910 It's 96 minus 1/2u. 861 00:42:27,840 --> 00:42:32,420 q star u, that's the red line, 96 minus 1/2qa. 862 00:42:32,420 --> 00:42:33,920 That's their best response function. 863 00:42:33,920 --> 00:42:36,827 Now once again, to remind you, I could simply skip to this step, 864 00:42:36,827 --> 00:42:39,160 but normally you'd have to solve through for both firms. 865 00:42:39,160 --> 00:42:41,950 They might not have identical best response functions, 866 00:42:41,950 --> 00:42:43,690 or symmetrical best response function. 867 00:42:43,690 --> 00:42:45,640 Well now we're golden. 868 00:42:45,640 --> 00:42:47,900 We have two equations and two unknowns. 869 00:42:47,900 --> 00:42:49,210 We know how to deal with that. 870 00:42:49,210 --> 00:42:51,520 And you solve them and you get the qa 871 00:42:51,520 --> 00:42:57,820 star equals qu star equals 64. 872 00:42:57,820 --> 00:43:01,150 You solve those two equations and two unknowns. 873 00:43:01,150 --> 00:43:06,300 So 64 is the solution of that system. 874 00:43:06,300 --> 00:43:08,860 What's the price? 875 00:43:08,860 --> 00:43:11,000 Someone raise their hand and tell me. 876 00:43:11,000 --> 00:43:13,040 What's the price? 877 00:43:13,040 --> 00:43:14,967 Without looking at the graph. 878 00:43:14,967 --> 00:43:15,467 Yeah? 879 00:43:15,467 --> 00:43:16,321 AUDIENCE: [INAUDIBLE] 880 00:43:16,321 --> 00:43:18,071 JONATHAN GRUBER: And how did you get that? 881 00:43:18,071 --> 00:43:20,705 AUDIENCE: [INAUDIBLE] 882 00:43:20,705 --> 00:43:22,580 JONATHAN GRUBER: You got to plug in 64 twice. 883 00:43:22,580 --> 00:43:23,872 A lot of people get this wrong. 884 00:43:23,872 --> 00:43:25,490 They'll say, oh, 339 minus 64. 885 00:43:25,490 --> 00:43:29,360 But no, it's 339 minus 128, because they're each flying 64 886 00:43:29,360 --> 00:43:32,400 and the price comes from the total demand in the market. 887 00:43:32,400 --> 00:43:36,733 So the price is $211. 888 00:43:36,733 --> 00:43:38,275 That's an important mistake to avoid. 889 00:43:38,275 --> 00:43:39,150 A lot of people get here. 890 00:43:39,150 --> 00:43:39,970 They'll be super excited. 891 00:43:39,970 --> 00:43:40,750 They're tired. 892 00:43:40,750 --> 00:43:42,790 They throw the 64 back at the demand equation. 893 00:43:42,790 --> 00:43:45,300 But remember, demand's a function of the total market. 894 00:43:45,300 --> 00:43:47,410 If symmetrically they're each doing 64, 895 00:43:47,410 --> 00:43:49,950 then the price is going to be $211. 896 00:43:49,950 --> 00:43:53,200 And that is the Nash or Cournot equilibrium. 897 00:43:53,200 --> 00:43:58,180 Both firms are happy to fly 64 flights at a price of $211. 898 00:43:58,180 --> 00:44:00,970 Neither firm wants to deviate. 899 00:44:00,970 --> 00:44:03,430 And you know that because you've maximized their profits. 900 00:44:07,830 --> 00:44:10,720 When United is flying 64, the profits of American 901 00:44:10,720 --> 00:44:13,300 are maximized at flying 64. 902 00:44:13,300 --> 00:44:15,640 When American's flying 64, the profits for United 903 00:44:15,640 --> 00:44:17,680 are maximized at flying 64. 904 00:44:17,680 --> 00:44:22,300 Therefore, that is the Nash or Cournot equilibrium. 905 00:44:22,300 --> 00:44:25,860 Now, when we get to reality, things might not always 906 00:44:25,860 --> 00:44:27,360 work out so neatly. 907 00:44:27,360 --> 00:44:28,830 Things might not be symmetric. 908 00:44:28,830 --> 00:44:31,380 You might also not have an equilibrium. 909 00:44:31,380 --> 00:44:34,410 How could you not have an equilibrium here? 910 00:44:34,410 --> 00:44:36,325 How could that happen graphically? 911 00:44:36,325 --> 00:44:37,200 What would that mean? 912 00:44:39,820 --> 00:44:40,408 Yeah? 913 00:44:40,408 --> 00:44:41,950 AUDIENCE: The curves don't intersect. 914 00:44:41,950 --> 00:44:42,867 JONATHAN GRUBER: Yeah. 915 00:44:42,867 --> 00:44:45,225 The best response curves might not intersect. 916 00:44:45,225 --> 00:44:46,600 You might not get an equilibrium. 917 00:44:46,600 --> 00:44:48,225 We don't know what the hell to do then. 918 00:44:48,225 --> 00:44:50,220 All chaos breaks loose. 919 00:44:50,220 --> 00:44:53,520 But you might not get an equilibrium in this market 920 00:44:53,520 --> 00:44:57,150 because the best response curves might not intersect. 921 00:44:57,150 --> 00:45:00,120 In reality, in life, you could have funky best response curves 922 00:45:00,120 --> 00:45:03,470 that are non-linear or you could have multiple intersections. 923 00:45:03,470 --> 00:45:05,840 We call it multiple equilibria. 924 00:45:05,840 --> 00:45:07,910 And then it becomes an indeterminate problem 925 00:45:07,910 --> 00:45:09,680 and you have to figure out which equilibrium they settle at, 926 00:45:09,680 --> 00:45:12,013 and that involves higher order mathematics that you talk 927 00:45:12,013 --> 00:45:13,770 about in more advanced classes. 928 00:45:13,770 --> 00:45:15,720 So this is the simplest, easiest cases. 929 00:45:15,720 --> 00:45:18,960 Symmetric case where linear best response functions intersect 930 00:45:18,960 --> 00:45:20,460 is your easiest case. 931 00:45:20,460 --> 00:45:22,950 But in general, the general way to solve this 932 00:45:22,950 --> 00:45:26,670 is the same, which is use the principle of game theory. 933 00:45:26,670 --> 00:45:29,640 Look, go back to the prisoner's dilemma. 934 00:45:29,640 --> 00:45:32,580 All we're doing here was creating best response 935 00:45:32,580 --> 00:45:33,220 functions. 936 00:45:33,220 --> 00:45:34,470 It's just there wasn't a line. 937 00:45:34,470 --> 00:45:36,060 It was just a point. 938 00:45:36,060 --> 00:45:38,387 The best response function was what we laid out here. 939 00:45:38,387 --> 00:45:40,470 All we did with these United and American examples 940 00:45:40,470 --> 00:45:43,420 was go to a continuum and develop best response functions 941 00:45:43,420 --> 00:45:46,060 around the best response point. 942 00:45:46,060 --> 00:45:46,560 Yeah? 943 00:45:49,758 --> 00:45:51,550 AUDIENCE: If the Nash equilibrium is always 944 00:45:51,550 --> 00:45:54,140 worse than when they're cooperating, 945 00:45:54,140 --> 00:45:57,560 why is it so hard to maintain a [INAUDIBLE]?? 946 00:45:57,560 --> 00:45:59,750 JONATHAN GRUBER: We'll talk about that next time. 947 00:45:59,750 --> 00:46:01,510 Other questions? 948 00:46:01,510 --> 00:46:02,630 OK, let's stop there. 949 00:46:02,630 --> 00:46:02,950 We'll come back. 950 00:46:02,950 --> 00:46:05,440 Next time we'll talk about, why don't we all just get along 951 00:46:05,440 --> 00:46:07,650 with Mr. Rogers once?