= Folk theorem for repeated games
A family of results describing the large set of <Nash equilibrium> <payoffs> available in indefinitely repeated interaction. For a finite game with observed past play, the discounted Nash version supports any feasible, strictly <individually rational payoff in a repeated game> when players are sufficiently patient.<Lecture 15: Repeated Games by Asu Ozdaglar>[Slide 24, Nash folk theorem; slides 25–27, permanent minmax punishments and the distinction from subgame perfection]{ref}
The mechanism is to prescribe a path and punish the first deviator by holding that player's future <payoff> to its <minmax payoff>. With <long-run average payoffs>, a finite gain disappears from the average; with discounting, the promised future loss must outweigh the gain. Weak boundary points require care when a stated theorem assumes strict inequalities. A construction proving a <Nash equilibrium> need not prove a <subgame perfect equilibrium>, because the punishers' continuation incentives may fail.
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