Repeated Prisoner's Dilemma

Game Theory · Axiom Academy

EXAMPLE Repeated Prisoner's Dilemma Finding the critical discount factor for sustained cooperation using grim trigger strategies Excellent work! You've completed this example on the repeated prisoner's dilemma. Here's what we learned: Cooperation can be sustained: In infinitely repeated games, players can support cooperation even when the stage game has defection as the dominant strategy, provided they are sufficiently patient. Critical discount factor: The threshold δ* = 1/4 tells us exactly how patient players must be. If δ ≥ 1/4, the grim trigger strategy forms a subgame perfect equilibrium. Grim trigger mechanics: The threat of permanent punishment (reverting to Nash equilibrium forever) makes deviation unprofitable when players value the future enough. General approach: To analyze any repeated game, compare the payoff from cooperation with the one-shot deviation gain plus subsequent punishment payoffs. This framework applies to many real-world situations: international agreements, business partnerships, and online reputation systems all rely on repeated interaction to sustain cooperation!

This is the written version of the interactive lesson above. See the full Game Theory course.