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Glossary · Game Theory

Folk Theorem (Repeated Games)

also: folk theorem · repeated games · infinitely repeated game · shadow of the future · tacit collusion

Definition

The folk theorem states that in an infinitely repeated game with sufficiently patient players, any feasible payoff profile giving each player at least their minmax value can be sustained as an equilibrium through credible punishment strategies. It is why tacit price discipline and promotional truces persist without any agreement, and why they collapse when discount rates rise.

The theorem earned its name because it circulated as unattributed folklore before Friedman (1971) and Fudenberg and Maskin (1986) formalized it. Its content is double-edged. On one side, repetition rescues cooperation: a firm that undercuts today can be punished tomorrow, so restraint becomes rational. On the other side, almost anything can be an equilibrium, so the theory predicts sustainability rather than selection. Three parameters govern the outcome in practice: the discount factor (how much players value future periods), the detection lag (how quickly a deviation is observed), and the severity and credibility of punishment. Quarter-end pressure, high customer-acquisition costs, and opaque competitor pricing all shorten the effective shadow of the future, which is when promotional wars break out.

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