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Grim trigger

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Grim Trigger is a trigger strategy in game theory for a repeated game, such as an iterated prisoner's dilemma. Initially, a player using Grim Trigger will cooperate, but as soon as the opponent defects (thus satisfying the trigger condition), the player using Grim Trigger will defect for the remainder of the iterated game. Since a single defect by the opponent triggers defection forever, Grim Trigger is the most strictly unforgiving of strategies in an iterated game.

Note that Tit for Tat, the commonly accepted optimal iterated game strategy, is also a trigger strategy, except that unlike Grim Trigger, it only "remembers" one move previous when determining whether to cooperate or defect.

In Robert Axelrod's book The Evolution of Cooperation, Grim Trigger is called FRIEDMAN.


 

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Topics in game theory

Definitions

Normal form game · Extensive form game · Cooperative game · Information set · Preference

Equilibrium concepts

Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy

Strategies

Dominant strategies · Mixed strategy · Grim trigger · Tit for Tat

Classes of games

Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design

Games

Prisoner's dilemma · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game

Theorems

Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's Theorem

Related topics

Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists

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