Prisoner's Dilemma
Two prisoners, separated, each offered a deal: testify against the other and go free while your partner gets ten years. If both testify, both get five years. If both stay silent, both get one year on lesser charges. The rational choice is to testify — regardless of what the other does. But if both are rational, both testify, and both get five years instead of the one they’d get by cooperating.
The structure, formalized by Albert Tucker in 1950, captures a fundamental tension: individual rationality can produce collective irrationality. Each player’s dominant strategy leads to an outcome worse for everyone than an achievable alternative.
The numbers tell the story. Assign payoffs: mutual cooperation is 3 each, mutual defection is 1 each, while the defector in a mixed outcome gets 5 and the cooperator gets 0. Whatever the other player does, defection pays better. If they cooperate, defection gives you 5 instead of 3. If they defect, defection gives you 1 instead of 0. Defect dominates. But mutual defection (1, 1) is worse than mutual cooperation (3, 3).
The dilemma is that no player can enforce mutual cooperation unilaterally. You can only choose your own action. If you cooperate, you’re at their mercy. Rational expectation that they’ll defect makes your defection inevitable — and vice versa.
The structure appears everywhere. Arms races: each country prefers being armed while the other disarms, but mutual armament is worse than mutual disarmament. Advertising: each company prefers advertising if competitors do, but universal advertising raises costs for everyone without changing market shares. Carbon emissions: each country prefers others reduce emissions while it continues, but universal continuation is worse than universal reduction.
Recognition of the structure is the first step toward solutions. The dilemma exists because the game is one-shot, anonymous, and lacks enforcement. Change any of those conditions and cooperation becomes possible.
Iteration changes everything. Robert Axelrod’s tournaments showed that in repeated prisoner’s dilemmas, cooperative strategies win. Tit-for-tat — cooperate first, then mirror the other’s previous move — outperformed aggressive strategies. The shadow of the future makes cooperation rational: defection today invites retaliation tomorrow.
But iteration requires recognizing the partner across rounds, remembering their history, and caring about future interactions. Anonymous one-shot interactions remain dilemmas. The structure predicts: strangers in crowds defect; neighbors in communities cooperate.
Related: [[game-theory]], [[nash-equilibrium]], [[mechanism-design]], [[antifragility]]