[SOUND] To model, cooperative and competitive behavior, we can use the Prisoner's Dilemma game. So this Prisoner's Dilemma game suggests, that there are two suspects in a major crime. And these two suspects, are held in different cells in the prison. There is enough evidence, to convict each of these suspects in a minor offense. But there is no enough evidence, to convict either of them of the major crime. Unless one of them will fink. And one of them, will actually tell and give some information about the second suspect. So, if both suspects stay quiet, both of them will be convicted for the minor offense and they will spend three months in jail, but if we, if one of them will fink. And will give some information about the second suspect. This guy will be freed and the second one will get 20 years in prison. So, if both of them will fink, each will spend five years in prison. So here each suspect faces a dilemma, was to cooperate with another suspect or to deflect. So we can actually represent this dilemma in a more formula way, as a decision matrix. So here, we see two suspects and if both stay quite, they will spend three months in prison. If both will fink, they will spend five years in prison. If one will fink and another one will stay quiet, the first guy will be freed and the second one, will spend 20 years in jail. If the second one, will fink and the first one will stay quiet. So we have as the opposite situation. So here, we have an incentive to cooperate, and also, we have an incentive to cheat. And this is a dilemma, for two suspects. So we can represent this, strategic game. In the most horrible way. So there are two suspects, two players. There's a set of actions. Each player can either cooperate or defect, so stay quiet or fink. As there is a clear, set of preferences so, if there's a best outcome for the suspect and the suspect finks and another suspect, is quiet and there is a reverse situation, when our suspect stayed quiet and another one finks. So, actually this situation models various, social situations, and there is an incentive to cooperate, but also in a sense of the free right. So prisoner dilemma, is a really great model that, can help us to understand how the people make decisions in group. So for example here, I illustrate another situation using the prisoner dilemma. So here is your landlord and the customer. A landlord and a student, for example. Student would like to rent room. If landlord provides a key and the customer pays, let's say $250 for the room the landlord gets a profit, $250. In case, if landlord gives a key, but the customer, by some reason, doesn't pay back. Actually, landlord can lose $250. So in case, if the landlord doesn't give the key and customer pays the money, the landlord can actually double the profit, because he can collect the money and also get an extra $250 from another customer. So, in case the landlord defects and the customer defects, nobody gets any money. So prisoner dilemma nicely illustrates very social situations, when we can cooperate or we can defect. And we have some incentives to cooperate. We also have some incentives to defect. So, what is the optimal decision, in the prisoner dilemma? You can apply a Nash equilibrium. So, informally, a set of strategy is a Nash equilibrium, if no player can do better by unilaterally changing his or her strategy. So here is a prisoner dilemma. Imagine that you're player one, so player two, for example, defects. In this case, it is rational to also defect, because otherwise you will lose $250. Imagine now that the player two cooperates. In this case, it is also rational. To defect, because otherwise you would get twice less amount of money. Since that pay of metrics is symmetrical, actually there is only one decision, that represent a Nash equilibrium. This is decision to defect. So, present dilemma suggests. There is only one rational solution for the dilemma, when both players defect. Actually, it brings us a very sad conclusion. It suggests that in the situation of the present dilemma, we always should defect. So if we have a group of cooperators, if suddenly, due to a mutation, for example, one defector, would appear in this group, this defector, will outperform the rest of the group. And with time, this group, will be overpopulated by defectors. So, this metaphor of mm, prisoner dilemma suggests, that there is only one rational solution for the prisoner dilemma, both players all players have to defect. So, it doesn't bring us any space for cooperation. And, actually, if we will come back to our world real life example. Prisoner dilemma can be applied to a nuclear war situation. And it was applied. So the idea of the recent dilemma, was used in the Rand Corporation, to model the decision, to bomb or not to bomb soviet union. So actually, the great Game Serials like John Nash and John Neumann. Were engaged into the analysis of the nuclear war, situation. And actually, at that time, game theory, suggested, to conduct a preemptive attack, the Soviet Union, before Soviet Union would develop own nuclear bomb so here, you see actual words of John Neumann, who suggested, if you say why not the bombs in tomorrow I say why not today? If you say today at five o'clock, I say why not at one o'clock? And actually Bertrand Russell. The famous mathematician of so interesting there is a game theory suggests, that in the case of the prisoner dilemma, you shouldn't cooperate, you should always defect. But come on, we all understand that cooperation brings some benefits, so, how can we find the place for cooperation using the game theory? Actually, we can show that corporations can bring some benefits, but to understand this, we have to introduce a new parameter omega, the probability that the players will meet again. This is so-called the shadow of the future parameter. So if the, omega is low, there is a very small chance that players will meet each other again. And in this case, it doesn't make sense to cooperate. But if omega is relatively large, it makes sense to cooperate, because using various strategies, you can actually reinforce cooperative behavior within the group and you can have a net benefit at the end. So let's make a look to the details of this idea. But first, let's try to understand the idea of the omega. So, for example, why do you fink. There is this interesting phenomena of a lame duck. So, you know, that elected officials at the end of their tenure, quite often are ignored by other politicians. So why is a president of a big country, at the end of his tenure is quite often ignored by other politicians? So what do you fink? Why is that happening? So perhaps because the omega is very small. So there is a very small chance that other politicians, will meet this person again, during the political process. That's why, they completely ignore this person as they would never cooperate with him. So, it is very rational, to not cooperate with the people. You would never meet again, and it is more rational to cooperate with other people, if there was a chance to meet these people again. So, the game theory suggests, that if the game is played only once, then each player, gets a higher payoff, from defecting than from cooperating, but, if the game is played repeatedly, for example, in the iterated prisoner dilemma game, there is a greater room for cooperation, so people can re-enforce cooperation, by certain behavioral strategies. So lets make a look to the strategies. So Sir Robert Axelrod conducted the very famous competition. So he compared different strategies, applied, for the, prisoner dilemma game. So this competition showed the tit for tat strategy, outperformed all other strategies, for the iterated prisoner dilemma game. So what is a tit for tat strategy? It's a very simple strategy. Cooperate in the first trial and in the next trial, repeat the behavior of the second player in the previous trial. So, you should cooperate in the first trial and if another person, second player, cooperates in the second trial, cooperates in the full ops trial also. If another person defects. Defect in the next trial, and so on. So we can characterize the tit for tat strategy by four important points. Be nice, so, cooperate in the first round. Reciprocate. Return defection for defection, so if we, another person defect, also defect in the next round. If person, a player, to cooperate. Cooperate in the next trial. Don't be envious. Be fair with your partner. And don't be too clever, because Robert Exler wrote competition shows that, very simple strategy like tit for tat strategy, outperforms, more complex strategies. So the tit for tat strategy is a, collectively stable strategy. So if the group of cooperators, uses the tit-for-tat strategy. This group, is resistant to the invasion, by their non-cooperators. So, if they chance to meet another person, again, is relatively high, if their omega is large. So reciprocation of the cooperation and the reciprocation of the defection, can stabilize the cooperative behavior of reasons of groups. So many studies and models show that the group of cooperators, can sustain cooperation within the group, using three important approaches. So first of all, the group can use direct reciprocity. So if, if, the defector defects cooperators should also defect, in the next trials. If the defector cooperates, cooperators should also cooperate in the next trial. So this strategy is a tit-for-tat strategy, can sustain cooperations in the group. Additionally, cooperators should leave in groups. The group of cooperators, can out perform the group of defectors. And finally, it is important to punish defectors. So you can punish those who defect, and also you can punish those who do not punish those who defect. So, with these different forms of punishment. You can dramatically increase cooperation within the groups. So let's try after the short break, to understand, how this process are implemented in our brains. [SOUND]
