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The Iterative Prisoner’s Dilemma

One of the more popular Game Theory ideas is the Prisoner’s Dilemma. Essentially this simple game has two players representing criminals who are separated and offered a choice. Either they can co-operate with their criminal partner by telling the police nothing or they can defect by turning the other criminal in. If they both co-operate the police can only get them on a minor charge and they both get one year in prison, if they both defect they each get ten years, but if one co-operates and the other defects, the defector gets off scot free while the co-operator gets 40 years. The result of this is that it’s always better to defect, because there are two possibilities, either your partner is co-operating in which case by defecting you go from getting one year to getting nothing, or your partner is defecting in which case you go from getting 40 years to getting ten.

What’s weird is that this is pretty obvious and everyone realises it, so everyone will defect, meaning that in a smart population everyone will be getting ten years, because that’s the best tactic. This unhappy situation is known as Nash’s Equilibrium. Meanwhile in a theoretical population of loyal dummies everyone is getting one year, despite their being totally wrong in their choices, the loyal stupid fools and their short sentences and general freedom. The fact that this shows what is clearly the worst tactic to be clearly the best tactic is therefore a little odd, and has led to an extension of the Prisoner’s Dilemma which seems to have been felt to clear up that weirdness, but has never sat entirely right with me, namely the Iterative Prisoner’s Dilemma.

The Iterative Prisoner’s Dilemma is, quite simply, that players engage in repeated rounds of the Prisoner’s Dilemma rather than just a single round. The idea being that if you can predict what your opponent is going to do over multiple rounds you’d do better and that process of prediction could be interesting. This was made physical with an iterative prisoner’s dilemma tournament for computer programs to test out the theory, what is considered interesting is that the winning program in that experiment was the shortest. It was a program called Tit for Tat and it