Repeated Games & Cartels

Played once, the Prisoner’s Dilemma looks hopeless. Played over and over with the same partner, things change. Now defecting today has a cost — the other player can punish you tomorrow. Cooperation becomes possible, sustained by the threat of future retaliation. That is the logic behind cartels: agreements among firms to restrict output and hold prices up.

Two strategies do most of the heavy lifting in repeated games. Tit-for-Tat cooperates on round 1, then copies what the opponent did the previous round. Cheat against it and you get one round of unanswered profit — then it retaliates. Cooperate again and it forgives the next round. Grim Trigger is harsher: it cooperates until the opponent cheats once, then defects forever. Tit-for-Tat is forgiving, Grim Trigger is unforgiving — both can sustain cooperation if players are patient enough.

The Folk Theorem in game theory says that in an infinitely repeated game — or one with an uncertain end — any outcome that gives each player at least their one-shot Nash payoff can be sustained as an equilibrium, provided players are sufficiently patient. Cooperation can be one such equilibrium. The catch is that many other outcomes can too, and which one prevails depends on whether the threat of punishment is credible. OPEC demonstrates both sides — large joint profits when discipline holds, frequent breakdowns when members exceed quotas.