Grim Trigger Strategy

A repeated-game strategy that cooperates until a specified defection and then defects permanently.

Grim trigger cooperates until a specified defection is observed, then switches permanently to defection. In an indefinitely repeated prisoner’s dilemma, the threat of losing future cooperation can support cooperative equilibrium when future payoffs matter enough and the monitoring and payoff assumptions hold.

For stage payoffs temptation T, mutual cooperation R, and mutual defection P, the usual condition is δ ≥ (T−R)/(T−P), where δ is the effective discount factor. With T=5, R=3, and P=1, the threshold is one half. This is conditional deterrence, not proof that no rational player will defect. Mistakes, misperception, changing incentives, and opportunities to renegotiate can all matter.

When to use it

Useful for analyzing repeated-game equilibria and the assumptions behind irreversible enforcement rules.

How it can help

Compare the incentive effect of losing future cooperation with the cost and reliability of permanent punishment.