Max Nisen in the Business Insider:
The basic version goes like this. Two criminals are arrested, but police can’t convict either on the primary charge, so they plan to sentence them to a year in jail on a lesser charge. Each of the prisoners, who can’t communicate with each other, are given the option of testifying against their partner. If they testify, and their partner remains silent, the partner gets 3 years and they go free. If they both testify, both get two. If both remain silent, they each get one.
In game theory, betraying your partner, or “defecting” is always the dominant strategy as it always has a slightly higher payoff in a simultaneous game. It’s what’s known as a “Nash Equilibrium,” after Nobel Prize winning mathematician and A Beautiful Mind subject John Nash.
In sequential games, where players know each other’s previous behaviour and have the opportunity to punish each other, defection is the dominant strategy as well.
However, on a Pareto basis, the best outcome for both players is mutual cooperation.
Yet no one’s ever actually run the experiment on real prisoners before, until two University of Hamburg economists tried it out in a recent study comparing the behaviour of inmates and students.
Surprisingly, for the classic version of the game, prisoners were far more cooperative than expected.
More here.