Game theory is a branch of applied mathematics and economics that models interactions in which each participant's payoff depends not only on their own choice but on the choices of others. Its modern foundations were laid by John von Neumann and Oskar Morgenstern in Theory of Games and Economic Behavior (1944), and extended by John Nash, whose 1950 paper introduced the Nash equilibrium — a profile of strategies from which no player can unilaterally deviate and improve their payoff.
A "game" is specified by three elements: the players, the strategies available to each, and the payoffs assigned to every combination of strategies. Games are typically classified along several axes:
- Cooperative vs. non-cooperative — whether binding agreements are enforceable.
- Zero-sum vs. non-zero-sum — whether one player's gain is exactly another's loss.
- Simultaneous vs. sequential — whether players move at the same time or observe prior moves.
- Complete vs. incomplete information — whether all players know the payoff structure.
Canonical examples include the Prisoner's Dilemma, which illustrates how individually rational choices can produce collectively suboptimal outcomes, and the Stag Hunt and Chicken games, used to model coordination and brinkmanship.
In international relations, game theory has been used to analyse arms races, nuclear deterrence (notably Thomas Schelling's work in The Strategy of Conflict, 1960), trade negotiations, alliance formation, and climate cooperation. Robert Axelrod's The Evolution of Cooperation (1984) used iterated Prisoner's Dilemma tournaments to argue that reciprocity ("tit-for-tat") can sustain cooperation without central enforcement.
Critics note that game-theoretic models rest on strong assumptions about rationality, common knowledge, and well-defined payoffs, which may not hold in real political environments. Behavioural game theory, advanced by scholars such as Colin Camerer, incorporates empirical findings on bounded rationality, fairness, and learning. Nobel Prizes in Economics have been awarded for game-theoretic work in 1994 (Nash, Harsanyi, Selten), 2005 (Aumann, Schelling), and 2012 (Roth, Shapley), among others.
Example
During the 1962 Cuban Missile Crisis, analysts at the RAND Corporation modelled the US–Soviet standoff as a game of "Chicken," informing Kennedy's calibrated naval quarantine strategy.
Frequently asked questions
Its modern formal foundation is credited to John von Neumann and Oskar Morgenstern, whose 1944 book Theory of Games and Economic Behavior established the field, though earlier contributions came from Émile Borel and Ernst Zermelo.
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