To turn the tables, victims must first realise that they are being exploited. If the “victim” keeps this up, a smart victimiser will realise they are getting hammered, says Press, and play more nicely. There is one other option: they can betray their victimiser at every turn, despite the heavy costs of doing so – guaranteed longer jail time. The pair show that the victim of the dirty play does best by always keeping shtum and accepting that their victimiser will get less time in jail ( Proceedings of the National Academy of Sciences, DOI: 10.1073/pnas.1206569109). They derived an equation that players must use at each turn to decide what to do on the basis of the previous turn. Press proved the strategy mathematically with Freeman Dyson of the Institute for Advanced Study in Princeton, New Jersey. And players who adopt his strategy end up spending much less time in prison than their opponents – in collaborative games, both players end up spending roughly equal time in prison. Now, William Press at the University of Texas at Austin says he has uncovered a strategy to win that is not collaborative. So essentially, the best strategy is to collaborate.

The way to minimise jail time under these conditions is usually to “play nice”: don’t snitch, on the assumption that your partner won’t either, and if they betray you then snitch on them in the next round, as a warning. The game becomes interesting when the same two partners play it over and over again. Even climate change negotiations can be thought of as a prisoner’s dilemma: no country wants to pay the cost of cutting emissions (keep shtum) if everyone else is going to keep on emitting (snitch). The dilemma has obsessed economists for over 50 years because it helps to explain why individuals sometimes don’t cooperate even when it is in their combined best interests to do so. But crucially, if criminal A thinks B won’t blab, it is in A’s best interest to snitch, as he will then walk free – at B’s expense. As a united pair, players do better if they both keep shtum. If both players betray each other, each gets a medium sentence.

But if one betrays the other, the snitch gets off scot-free while their partner suffers a long sentence. In the prisoner’s dilemma, if both players keep quiet, each gets a brief sentence. Whereas most winning strategies involve playing nice, the new method relies on playing dirty. Now, a pair of mathematicians have identified a new way of playing the game that allows a player to do significantly better than their opponent. This “prisoner’s dilemma” is a classic psychology game used to study how collaboration evolves in animal societies. Should you keep quiet or betray your partner? They interrogate you in separate rooms and offer you a deal. The police have arrested you both, but they don’t have enough evidence to lock you up and throw away the key unless one of you rats out the other. PICTURE this: you and a partner have committed a crime.

Fun games for inmates