In game theory, an iterated game (or repeated game) is a strategic interaction played more than once by the same actors, so that each player's choices in one round can depend on the history of previous rounds. Unlike a one-shot game, iteration creates a "shadow of the future": the prospect of continued interaction changes the payoff calculus and can sustain cooperative outcomes that would be irrational in a single play.
The canonical example is the iterated Prisoner's Dilemma. In a single round, mutual defection is the dominant-strategy equilibrium. When the game is repeated indefinitely (or with unknown end), strategies that reward cooperation and punish defection—such as tit-for-tat, made famous by Robert Axelrod's computer tournaments in 1980 and his 1984 book The Evolution of Cooperation—can outperform pure defection. The folk theorem formalizes this: in infinitely repeated games with sufficiently patient players, a wide range of payoffs (including cooperative ones) can be supported as subgame-perfect equilibria.
Key distinctions matter:
- Finitely repeated games with a known endpoint often unravel through backward induction back to the one-shot equilibrium.
- Infinitely repeated or indefinitely repeated games (with a continuation probability) sustain cooperation more robustly.
- Discount factors capture how much players value future payoffs; higher patience widens the set of cooperative equilibria.
In international relations, iterated-game logic underpins much of neoliberal institutionalism. Robert Keohane's After Hegemony (1984) argued that international institutions help states cooperate by lengthening shadows of the future, increasing transparency, and linking issues across repeated encounters—mitigating the collective-action problems described by realists. The framework is applied to arms control, trade reciprocity under the GATT/WTO, climate negotiations, and tit-for-tat tariff cycles. Critics note that iteration alone does not guarantee cooperation: outcomes depend on information, the number of players, enforcement, and whether actors actually expect to meet again.
Example
During the US–Soviet arms control negotiations leading to the 1987 INF Treaty, both superpowers behaved as players in an iterated game, using verification regimes and reciprocal concessions to sustain cooperation across decades of repeated interactions.
Frequently asked questions
Repetition creates a 'shadow of the future': defecting today invites retaliation tomorrow, so patient players can sustain cooperation as an equilibrium when single-shot defection would dominate.
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