Trigger Strategies

Game Theory · Axiom Academy

Unit 4: Repeated Games - How the threat of punishment sustains cooperation 1. What is a Trigger Strategy? A trigger strategy (also called a grim trigger strategy ) is a simple but powerful approach to repeated interactions: Start by cooperating in the first period Continue cooperating as long as all players have always cooperated If any player defects even once, switch to defection forever The strategy is "triggered" by a single defection, leading to permanent punishment. This creates a credible threat that can sustain cooperative behavior. 2. History-Dependent Strategies Trigger strategies are a prime example of history-dependent strategies , where current actions depend on past play: Memory: Players remember the complete history of the game Conditioning: Actions are contingent on observed behavior Punishment phase: Once triggered, the punishment is permanent and irreversible Credibility: The punishment must be a best response (often a Nash equilibrium of the stage game) In the classic Prisoner's Dilemma, the trigger strategy prescribes cooperation until someone defects, then switches to the Nash equilibrium (defect, defect) forever. 3. Trigger Strategies in Action Let's see how trigger strategies work over multiple periods. Watch as players cooperate successfully, then observe what happens when one player defects: 4. When Trigger Strategies Work

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