Prisoner’s Dilemma

The Prisoner’s Dilemma, from game theory, originally stated as:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

If they betray each other, both will serve 2 years in prison.
If they remain silent, both will serve 1 year in prison (on the lesser charge).
If one betrays and the other remains silent, the betrayer will be set free and the silent one will serve 3 years in prison.

In the iterated version of this game, a prisoner has the opportunity to retaliate against a previous betrayal. A variant of the iterated Prisoner’s Dilemma is the Peace War Game, where players can compete (war) or cooperate (peace). From both of these iterated games altruistic strategies emerge where the best possible outcome is to maximize cooperation (peace) amongst players.

In game theoretic terms, a successful strategy must be Nice (not defect before the other player does), Retaliating, Forgiving, and Non-envious. The most successful and simple strategy to these iterated games is known as Tit for Tat, and is similar to reciprocal altruism from evolutionary biology. In these strategies the player is “Nice” and will start with cooperation and will defect (war) only in retaliation. The primary difference between these two strategies is that Tit for Tat is forgiving (it repeats the opponents strategy from the previous round).

In real-life scenarios, Tit for Tat as a strategy has the advantage of being transparent and predictable. In practice Tit for Tat allows for cooperation with blind altruists (with identical altruistic behavior), while not being taken advantage of by bad actors, and while being forgiving the moment a bad actor switches to a cooperative (peace) strategy.

In order to avoid a death spiral, a Tit for Tat strategy can be modified to occasionally “forgive” even after previous betrayals. In this case one responds to altruism with predictable cooperation, but responds to betrayal with unpredictable retaliation.