Let's now talk about the most famous example in game theory. It's called the Prisoner's Dilemma. And if you watch movies, film noirs you probably have seen something like that on TV. Let's see if it works or not. So two suspects are accused of committing a crime. They're arrested and they are placed in separate cells so that they cannot communicate. They are interrogated separately. Communication here will play an important role, we'll see how. So the prosecutor knows that if they confess, it will be much easier to be convicted. The case will finish much faster. So the prosecutor makes an offer to both of them, if they confess, they will receive a lighter sentence. So the life of everyone is going to be easier. Here's the game. Let's assume that if they both confess, they get five years in jail, both of them. If they both deny the allegations, then each one of them will get only two years in jail because it will be difficult to convict them and they will probably be convicted for a lesser crime. The interesting point in Prisoner's dilemma, is what happens if one prisoner denies and the other confesses? If you confess while your partner denies, then you get only one year in jail because you helped and the other one because they didn't help goes to jail for 10 years. So this a very interesting fact of the game. So what is best for you to do? Well, if the two players they judge together, they could communicate and they would commit to what they're doing, the first thing to do is that they will both deny. So this would be the social optimal because, if you look at this payoffs in these meetings you will see that they are negative. So we're looking for the smallest absolute value now. You don't want to go to jail for a long time. You want to keep your payoffs as small in absolute value as possible. So the best would be if we both deny. But, there is an even better case. The better case is that, if I convince you to deny but I confess, because I sent you to jail for 10 years and then I get out after only one year. Let's see how this can be enforced. If you look at the matrix very carefully, we will see that the point that is underlined is the point confess, confess. This is the Nash equilibrium. We have seen it before that the Nash equilibrium, usually is not the socially optimal. In our case, it's socially suboptimal, of course. So it's not the best that these two players can do together. Each player would play D if only there was some way to be sure that the other player would also follow and play also D. They would both deny in these games. Is this possible? If there is no commitment mechanism enforced in this game, there is no way for me to commit that, Yes I will play deny, here I'm signing a paper to use that is a binding promise that that I will play deny. Then you can do the same and if this can happen, this commitment mechanism existed, we would both play deny. But the cops are not silly, they put them in different cells so they cannot communicate and they can have a binding agreement. They interrogate them separately so once they come to the decisions, they will be like, "Okay, how should I think?" If I deny, I have a chance of getting only two years and this will be best for both of us because also the other person will get only two years. But, if I deny, I leave myself open, I expose myself to exploitation because if the other person plays confess, I will go to jail for 10 years. This fear of exposure by yourself makes you deviate alone to a point that is socially suboptimal. So they both get to the Nash equilibrium, Nash equilibrium is confessed here, gives you five years in jail, while they could collude, they could come to an agreement. Collusion is a very important word, keep it in mind because we'll talk about how firms use that in several lectures. The collusion point here is that they both deny, gives you only two years. But there are also two cheating points. Convince the other person to deny and you confess and then you get only one while your opponent gets 10. This would be the sweetest outcome for you. But the problem now, is that we end up at this socially suboptimal equilibrium of minus five and minus five. Question that we ask very often, does it work? I will show you in a real life example personal story, right after this.