0:00:06.086,0:00:07.576 >> Let's talk a little[br]bit about game theory. 0:00:08.406,0:00:10.896 Some times in economics[br]people want to be able 0:00:10.896,0:00:12.706 to describe situations 0:00:12.706,0:00:15.096 that involve what we call[br]strategic interaction. 0:00:15.936,0:00:17.806 Strategic interaction just means 0:00:17.806,0:00:22.076 that now not only does your pay[br]off, your profit, your utility, 0:00:22.076,0:00:25.856 how ever you want to think about[br]it depend on your own choices 0:00:26.286,0:00:29.376 but it also depends on the[br]choices of other people 0:00:29.376,0:00:32.916 in your market, in your[br]industry and so on and so forth. 0:00:33.996,0:00:37.096 Typical examples of strategic[br]interaction usually involves 0:00:37.096,0:00:39.486 decision among firms[br]regarding whether 0:00:39.486,0:00:42.246 to cooperate or to compete. 0:00:42.906,0:00:44.356 We're going to go[br]over and example 0:00:44.356,0:00:46.396 that has a slightly[br]different context known 0:00:46.396,0:00:49.696 as the prisoner's dilemma where[br]people are deciding whether 0:00:49.696,0:00:52.336 or not to confess to[br]a particular crime. 0:00:52.476,0:00:56.476 The set up of the prisoner's[br]dilemma is a tad bit contrived 0:00:56.576,0:00:57.556 but it goes as follows. 0:00:58.456,0:01:01.376 Imagine a situation in[br]which two people are brought 0:01:01.576,0:01:03.236 in for supposedly[br]committing a crime. 0:01:04.066,0:01:06.306 Now these two people are[br]held in separate cells 0:01:06.306,0:01:08.506 so they can't talk to[br]each other and even 0:01:08.506,0:01:11.316 if they could they couldn't[br]somehow contract on whether 0:01:11.316,0:01:12.716 or not they were going[br]to confess to the crime. 0:01:14.236,0:01:16.356 The people are then[br]brought in individually 0:01:16.506,0:01:19.326 and asked do you confess[br]or do you not confess? 0:01:20.656,0:01:23.606 We can represent the pay off's[br]to that sort of situation 0:01:24.296,0:01:25.526 in a table as follows. 0:01:25.916,0:01:31.456 You'll notice here that we[br]have player 1 and player 2. 0:01:31.456,0:01:33.656 I made things nicely color coded 0:01:33.656,0:01:37.756 such that we have player 1's[br]pay off's in terms of utility 0:01:38.796,0:01:43.136 in blue to match play 1 and[br]player 2's pay off's in terms 0:01:43.136,0:01:45.586 of utility in green here. 0:01:47.106,0:01:51.386 So you'll notice that if neither[br]player confesses they just sit 0:01:51.386,0:01:54.616 there and hold tight, they[br]each get a pay off of 10. 0:01:55.896,0:01:59.566 If the first guy keeps quiet[br]and the second guy rats him 0:01:59.566,0:02:05.216 out the second guy gets 15 while[br]the first player gets nothing. 0:02:06.546,0:02:10.756 The opposite happens here[br]if the first player rats 0:02:10.756,0:02:13.756 out the second one, now[br]the first player gets 15 0:02:14.156,0:02:15.516 and the second player[br]gets nothing. 0:02:16.566,0:02:19.556 And if they both try to rat[br]each other out, they both end 0:02:19.556,0:02:24.156 up with 5 meaning they're better[br]off than if they just sat here 0:02:24.156,0:02:27.066 and had the other guy[br]rat him out but not quite 0:02:27.066,0:02:30.786 as well off collectively[br]as if they both kept quiet. 0:02:31.626,0:02:38.236 The question then becomes given[br]this structure what's going 0:02:38.236,0:02:38.606 to happen. 0:02:38.606,0:02:40.746 In reality both players are[br]making the decision of whether 0:02:40.856,0:02:44.996 or not to confess at the same[br]time but let's just pretend 0:02:44.996,0:02:46.816 that they can guess or somehow[br]know what the other person is 0:02:46.816,0:02:50.376 going to do and we can ask a[br]number of hypothetical questions 0:02:50.706,0:02:54.346 as to what the best response[br]is for these players would be. 0:02:54.346,0:02:57.206 So let's take the[br]first case here, 0:02:58.116,0:03:02.256 say if player 1 confesses[br]what should player 2 do? 0:03:02.256,0:03:04.996 In other words what's[br]player 2's best response? 0:03:06.366,0:03:07.566 Well, we can go over here, 0:03:08.286,0:03:11.746 we say if player 1[br]confesses we're somewhere 0:03:11.856,0:03:18.286 in the bottom here and player 2[br]can either get zero by holding 0:03:18.286,0:03:22.456 out and being quiet or he[br]can get 5 by confessing also. 0:03:23.506,0:03:28.516 Five is strictly better than[br]zero so if player 1 confesses, 0:03:28.566,0:03:36.746 player 2 also wants to confess. 0:03:37.086,0:03:39.116 Now what about if[br]player 1 doesn't confess, 0:03:40.066,0:03:44.556 well if player 1 doesn't[br]confess we're up here 0:03:44.766,0:03:48.196 so player 2 again has two[br]options, he can get 10 0:03:48.196,0:03:53.616 by keeping quiet or he can get[br]15 by ratting out his buddy. 0:03:54.666,0:03:59.146 So 15 is better than 10 so[br]if player 1 doesn't confess, 0:04:00.776,0:04:08.766 player 2 still should confess. 0:04:08.886,0:04:13.886 Notice here that's interesting[br]that player 2 his best option is 0:04:13.886,0:04:17.736 to confess regardless[br]of what player one does 0:04:18.326,0:04:21.256 or alternatively put[br]player 2's best option is 0:04:21.326,0:04:25.016 to confess regardless of what he[br]thinks player 1 is going to do. 0:04:26.256,0:04:30.336 This type of situation is[br]called a dominant strategy 0:04:30.736,0:04:33.126 in that confess is[br]a dominant strategy 0:04:33.186,0:04:35.886 for player 2 meaning it's[br]always the best regardless 0:04:35.886,0:04:36.826 of what the other guy does. 0:04:37.976,0:04:40.966 Think about this the other way[br]around, say we make some guesses 0:04:40.966,0:04:44.446 as to what player 2 is going[br]to do and then when we say 0:04:44.446,0:04:47.406 in each case what's player 1's[br]best response in that situation. 0:04:49.136,0:04:50.926 So if player 2 confesses, 0:04:51.526,0:04:54.916 what's the best thing[br]for player 1 to do? 0:04:55.166,0:04:57.726 Say if player 2 confesses[br]we're over here 0:04:57.726,0:05:02.646 on the right somewhere we[br]say player 1 can either get 5 0:05:02.996,0:05:07.886 by confessing or 0 for being[br]quiet this problem is looking 0:05:07.886,0:05:11.126 strangely familiar, say[br]well 5 is better than 0 0:05:11.376,0:05:16.966 so player 1 is going[br]to want to confess. 0:05:18.696,0:05:22.236 Now if player 2 doesn't[br]confess what should player 1 do? 0:05:23.966,0:05:26.916 So if player 2 doesn't[br]confess, we're over here 0:05:26.916,0:05:30.736 on the left somewhere and[br]player 1 can either get 10 0:05:30.986,0:05:34.006 by being quiet or 15 by[br]ratting out his buddy, 0:05:34.516,0:05:44.836 well 15 is greater than 10 so[br]he's going to want to confess. 0:05:44.966,0:05:46.936 Notice here that[br]because we confessed 0:05:47.076,0:05:51.626 in both cases confessing[br]is also a dominant strategy 0:05:52.066,0:05:53.686 for player 1. 0:05:54.986,0:05:58.836 So here I've circled player[br]2's best responses in green 0:05:59.316,0:06:02.996 and I've circled player[br]1's best responses in blue 0:06:04.126,0:06:06.906 and you'll notice there's one[br]place here where they over lap 0:06:07.606,0:06:11.886 to say that in this situation[br]where both parties confess both 0:06:11.886,0:06:15.176 of them are responding[br]as best they can 0:06:15.786,0:06:18.506 to what they think the other[br]person is going to be doing. 0:06:19.736,0:06:22.536 We say that this situation[br]here is what's called a Nash 0:06:22.726,0:06:27.656 equilibrium; more formally put a[br]Nash equilibrium is a situation 0:06:27.656,0:06:31.446 where each player's[br]action is the best response 0:06:31.886,0:06:34.506 to the other player's actions. 0:06:35.256,0:06:38.486 In a situation where the players[br]are all moving simultaneously 0:06:38.756,0:06:41.926 this basically means that[br]each player is reacting best 0:06:42.096,0:06:44.276 to what they think the[br]other person is going to do 0:06:44.746,0:06:46.416 and they're actually[br]right in their guess 0:06:46.416,0:06:48.476 of what the other[br]person is going to do. 0:06:55.516,0:07:01.996 [ Pause ] 0:07:02.496,0:07:06.796 Notice here that the equilibrium[br]outcome actually...it doesn't 0:07:06.796,0:07:09.736 look as good as it could[br]because here we're saying 0:07:09.736,0:07:12.556 that any equilibrium when[br]people are acting according 0:07:12.556,0:07:15.556 to their own best interest each[br]of them ends up with a payout 0:07:15.556,0:07:19.396 of 5 where as if they only[br]cooperated they would each get a 0:07:19.396,0:07:21.706 payout of 10. 0:07:21.786,0:07:26.786 We can say here that there can[br]be a perato improvement going 0:07:26.786,0:07:30.836 from both parties confessing[br]to both parties staying quiet 0:07:31.376,0:07:33.586 in that both parties[br]would be made better off 0:07:34.406,0:07:36.286 and nobody would[br]be made worse off. 0:07:37.666,0:07:39.836 Unfortunately, due to[br]the competitive nature 0:07:39.836,0:07:42.736 of the this game that's[br]not what's going to result 0:07:42.736,0:07:46.126 because it's really hard when[br]there's no contracting involved 0:07:46.806,0:07:50.716 to guarantee regardless of[br]what the other party says then 0:07:50.716,0:07:52.556 when it comes down to it[br]they're actually going 0:07:52.556,0:07:54.226 to cooperate given that it's 0:07:54.226,0:07:57.286 in their interest[br]individually to not cooperate. 0:07:58.446,0:08:00.206 So one question that[br]economists like to think 0:08:00.206,0:08:04.056 about is then how can[br]cooperation be sustained 0:08:04.056,0:08:04.976 in the real world? 0:08:05.606,0:08:07.256 Well, one thing that's[br]important to remember here is 0:08:07.256,0:08:11.536 that in the real world this[br]game isn't played just once, 0:08:12.026,0:08:13.496 when you have firms interacting 0:08:13.496,0:08:16.956 with each other people making[br]these decisions often times they 0:08:17.016,0:08:19.676 have the chance to make the[br]decisions over and over and over 0:08:19.676,0:08:24.586 so when you have what's called[br]a repeated game you might have a 0:08:24.586,0:08:27.096 situation where people[br]start testing out the waters 0:08:27.246,0:08:30.196 to say well maybe if I[br]cooperate the other guy's going 0:08:30.196,0:08:32.866 to cooperate and then[br]we can keep this going 0:08:33.926,0:08:39.106 because to cooperate here and[br]hope for the best outweighs, 0:08:39.106,0:08:41.216 you know there's this[br]threat of well if you try 0:08:41.216,0:08:44.466 to screw me one time we're[br]reverting back here actually 0:08:44.466,0:08:47.666 gives in the long term an[br]incentive to cooperate. 0:08:48.836,0:08:51.516 So like I said it seems a little[br]bit artificial to be talking 0:08:51.516,0:08:54.956 about this context of[br]prisoners being interrogated 0:08:55.716,0:09:00.706 because really we're[br]talking about economics. 0:09:01.846,0:09:08.066 But it's very easy to see how[br]this situation could be relevant 0:09:08.066,0:09:10.756 in an economic context by just[br]replacing the intuition behind 0:09:10.756,0:09:11.276 some of the choices. 0:09:11.276,0:09:14.006 So what I did here is[br]set up the identical game 0:09:14.226,0:09:21.536 and have this model as[br]still player 1 and player 2 0:09:21.536,0:09:25.526 but now they have the[br]choice of whether or not 0:09:25.686,0:09:26.656 to cooperate or to compete. 0:09:26.656,0:09:32.316 And you can see here they'd both[br]do better off by cooperating 0:09:32.316,0:09:35.156 but they also all have the[br]private incentive to compete. 0:09:35.436,0:09:38.406 And you can notice here 0:09:38.406,0:09:41.486 that this situation is[br]actually pretty realistic 0:09:42.926,0:09:47.816 because at least in the United[br]States firms are not allowed 0:09:47.846,0:09:49.226 to contract on whether or not[br]they're going to cooperate, 0:09:49.256,0:09:50.096 that's called collusion,[br]it's illegal. 0:09:50.126,0:09:51.116 So they really are[br]simultaneously making 0:09:51.146,0:09:52.376 independent choices as[br]to how much to cooperate 0:09:52.406,0:09:52.976 with their ''competitors''.