Folk Theorem

The folk theorem of repeated games states that in an infinitely repeated game, any payoff vector that is both feasible and individually rational can be sustained as a Nash equilibrium outcome. The theorem dissolves the apparent conflict between individual self-interest and collective welfare: when the shadow of the future is long enough, cooperation does not require altruism, only the credible threat of punishment.

The result is called 'folk' because it was part of the oral tradition of game theory for years before formal proofs were published. It applies to both infinitely repeated games and finitely repeated games with uncertain endpoints. The key condition is that players must value future payoffs sufficiently — captured by the discount factor — that the threat of future retaliation outweighs the temptation to defect today.

The folk theorem is not merely a mathematical curiosity. It is the formal justification for every handshake deal, every reputation-based market, and every unwritten rule that sustains cooperation without external enforcement. The theorem proves that order can emerge from the structure of interaction itself.