Finitely Repeated Games

Game Theory · Axiom Academy

LESSON Finitely Repeated Games Understanding backward induction and why cooperation unravels in finitely repeated games 1. Games with Known Finite Horizon A finitely repeated game consists of a stage game played exactly T times, where T is known to all players from the start. Fixed and known number of rounds: T = 1, 2, 3, ..., T After round T, the game ends definitively Players know exactly when they're in the final round No uncertainty about game continuation 2. Backward Induction from Round T Backward induction analyzes the game by starting from the final round and working backward to determine optimal strategies at each stage. The Logic: In round T (the last round), there are no future rounds to consider, so players simply play the stage game Nash equilibrium. Knowing this, what should they do in round T-1? And so on, working backward... 3. The Unraveling Argument in Prisoner's Dilemma In a finitely repeated Prisoner's Dilemma, cooperation inevitably unravels through backward induction. Round T: No future consequences exist, so both players defect (stage Nash equilibrium). Round T-1: Since both will defect in round T regardless, there's no future cooperation to sustain, so both defect in T-1. Continuing backward: The same logic applies to every round, unraveling cooperation all the way back to round 1. 4. When Finite Repetition CAN Support Cooperation

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