Game theory: Prisoners dilemma

I recently got interested in game theory and I finally understood one of most popular examples in it:  Prisoners Dilemma. I find it quite exciting so I will explain it to you in the most simple way possible.

Prisoner’s Dilemma: Basically, Billy Bob and Joe are caught while robbing Caesar’s palace in Las Vegas. Both Billy Bob and Joe are about to be sent to jail, but the problem is that Jack, the police officer, does not have enough evidence to put them both in. Jack goes to Billy Bob and Joe, each locked up in different cells and gives them the following choices : confessing that the other actually robbed the casino or being quite about it. Here are the possible outcomes:

  • If both of the convicts keep quite, they both go to jail for 4 years
  • If one ratts or tells the police that the other did the crime and the other one keeps quite, the one who spoke up goes to jail for a year, while the more reticent one goes for 15 years
  • If both the convicts say that their partner actually committed the crime, both go to jail for  6years

So the question is: What should Billy Bob and Joe do? It seems obvious that both should keep quite since that outcome has the least number of years. That, however, is probably something that Billy Bob or Joe would not do. The reason for that action is that it is not favorable for either of them to be quiet. To explain why this is the case, take a look at my awesome picture below:

In the picture, it is clear that it is better for both of Billy Bob and Joe to rat the other out because the jail time is less. For example, if we ignore Joe’s descision and only look at the numbers availabile to Bob, he would choose the top row since 6 years is better than 10 years and 1 year is better than 4 years. Joe has the exact same issue. So if we suppose that both crooks are only caring about themselves, it is better to rat than be quite. Even if Bob and Joe were smart enough to figure this out, they would still bail the other out since they would have the uneasiness of thinking “hey my partner might have lied to me” So they both end up doing 6 years instead of 4 if they had kept quiet.

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