A grim trigger is a history-dependent pure strategy in a repeated game that switches permanently to punishment after a trigger event. In the iterated prisoner's dilemma above, the trigger is any player's observed defection, and punishment is always defect. Unlike Tit for tat, grim trigger never restores cooperation after the opponent cooperates again. Whether mutual grim trigger is a subgame perfect equilibrium depends on the stage payoffs, discount factor, and monitoring assumptions; it is not an unconditional property of the rule. See Ozdaglar, lecture 15, slides 12–15.
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The Grim Trigger is a concept in game theory, particularly in the study of repeated games. It refers to a specific strategy employed by a player in response to the actions of their opponent. The Grim Trigger strategy is characterized by its severe punishment mechanism for any deviation from cooperative behavior. Here’s how it works: 1. **Cooperation Phase**: Players start by cooperating with each other in the repeated game.