Grim Trigger Strategy
What is Grim Trigger Strategy?
A grim trigger strategy cooperates until the opponent defects even once, then punishes by defecting forever after.
It is the harshest trigger strategy in a repeated game: a single defection triggers permanent retaliation. If players value the future enough (a high discount factor), the threat of eternal punishment makes cooperation a subgame-perfect equilibrium. Economists use it to explain how cartels sustain collusion without legal enforcement, since cheating once destroys all future cooperative profits.
Grim Trigger Strategy: a worked example
Two quarry firms each earn $60 a year while both restrain output. Undercutting once pays $100 that year, after which grim trigger leaves them competing at $40 forever. Writing the discount factor as d, the honest path is worth 60 / (1 - d) and cheating is worth 100 + 40d / (1 - d). Cooperation survives when 60 is at least 100 - 60d, which gives d of at least 2/3. Check it: at d = 0.75, honesty pays 60 / 0.25 = $240 against $220 from cheating, so the cartel holds. At d = 0.5, honesty pays $120 against $140, so it breaks.
The mistake students make with grim trigger strategy
Students often object that grim trigger is irrational because nobody would actually punish forever once it hurts them too. In the standard infinitely repeated game the threat is credible: permanent mutual defection is itself an equilibrium of every remaining subgame, so carrying it out really is a best response. The genuine weakness is different. Grim trigger cannot recover from an accident, and a single misread price cut ends cooperation permanently, which is why real cartels use punishment phases of finite length.
Grim Trigger Strategy questions
What is the difference between grim trigger and tit-for-tat?
Grim trigger and tit-for-tat differ in forgiveness. Tit-for-tat answers one defection with exactly one round of defection and returns to cooperating as soon as the opponent does. Grim trigger never returns, since one defection ends cooperation for good. That makes grim trigger the harsher deterrent on paper and the more fragile rule in practice, because it cannot tell a deliberate cheat from a mistake.
Why do cartels use grim trigger strategies?
Cartels lean on grim trigger threats because a collusive agreement cannot be enforced in court. No member can sue another for undercutting the agreed price, so the only penalty available is the loss of future collusive profit. A standing threat to compete forever after any price cut turns that lost future into a cost the cheater pays immediately, which holds the arrangement together without any contract.
When does grim trigger fail to sustain cooperation?
Grim trigger fails when players discount the future heavily, when the game has a known final round, or when they cannot observe each other clearly. If a rival's apparent price cut might be a reporting error or a short promotion, permanent punishment fires on noise and wrecks a working arrangement, so firms tend to adopt punishment phases with a fixed length instead of an endless one.
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