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.^[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.