PICTURE this: you and a partner have committed a crime. The police have arrested you both, but they don鈥檛 have enough evidence to lock you up and throw away the key unless one of you rats out the other. They interrogate you in separate rooms and offer you a deal. Should you keep quiet or betray your partner?
This 鈥減risoner鈥檚 dilemma鈥� is a classic psychology game used to study how collaboration evolves in animal societies. 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. Whereas most winning strategies involve playing nice, the new method relies on playing dirty.
In the prisoner鈥檚 dilemma, if both players keep quiet, each gets a brief sentence. But if one betrays the other, the snitch gets off scot-free while their partner suffers a long sentence. If both players betray each other, each gets a medium sentence. As a united pair, players do better if they both keep shtum. But crucially, if criminal A thinks B won鈥檛 blab, it is in A鈥檚 best interest to snitch, as he will then walk free 鈥� at B鈥檚 expense.
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The dilemma has obsessed economists for over 50 years because it helps to explain why individuals sometimes don鈥檛 cooperate even when it is in their combined best interests to do so. Even climate change negotiations can be thought of as a prisoner鈥檚 dilemma: no country wants to pay the cost of cutting emissions (keep shtum) if everyone else is going to keep on emitting (snitch).
The game becomes interesting when the same two partners play it over and over again. The way to minimise jail time under these conditions is usually to 鈥減lay nice鈥�: don鈥檛 snitch, on the assumption that your partner won鈥檛 either, and if they betray you then snitch on them in the next round, as a warning. So essentially, the best strategy is to collaborate.
Now, says he has uncovered a strategy to win that is not collaborative. And players who adopt his strategy end up spending much less time in prison than their opponents 鈥� in collaborative games, both players end up spending roughly equal time in prison.
Press proved the strategy mathematically with , New Jersey. They derived an equation that players must use at each turn to decide what to do on the basis of the previous turn. 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 ().
There is one other option: they can betray their victimiser at every turn, despite the heavy costs of doing so 鈥� guaranteed longer jail time. If the 鈥渧ictim鈥� keeps this up, a smart victimiser will realise they are getting hammered, says Press, and play more nicely. To turn the tables, victims must first realise that they are being exploited.
Press says he doesn鈥檛 know of examples of his strategy being used in the real world. But it could conceivably play out in climate negotiations, whereby some nations might inadvertently proffer just the right mixture of emissions cuts and stubborn inaction, forcing other countries to take on a disproportionate share of the costs.
