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Folk theorem

In a relationship that lasts long enough between players who are patient enough, almost any outcome that beats what each can guarantee alone can be held in place by the threat of punishment.

In a relationship that lasts long enough between players who are patient enough, almost any outcome that beats what each can guarantee alone can be held in place by the threat of punishment.

Often misread asReading the folk theorem as proof that repetition delivers cooperation, and filing it as good news about long relationships.

How to see it

Almost anything is an equilibrium once players are patient enough

The folk theorem says that in an infinitely repeated game with sufficiently patient players, essentially any average payoff giving each player at least what they could guarantee themselves alone can be supported as an equilibrium. Cooperation is one of those outcomes. So is a lopsided arrangement where one side does most of the giving, and so is something close to the bad one-shot outcome.

The checkIt cuts both ways. What it really says is that equilibrium stops being a sharp prediction once players are patient, because almost everything individually rational becomes supportable.
Try itWrite down three different long-run average outcomes of a repeated prisoner's dilemma, including one where player one cooperates far more often than player two. Ask which of them the folk theorem rules out. Only those paying someone less than their one-shot safe payoff.

Games that show it

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When it stops being true

Easily confused with

Sources