Game theory

A strategic situation arises when the result for one decision-maker depends partly on what others do. A game-theoretic model typically specifies players, the strategies available to them, and the payoffs or preferences attached to possible outcomes. It may also describe when choices are made and what each player knows. Simultaneous decisions are often represented in a payoff table; a sequence of moves can be represented as a tree. In this technical sense, a “game” need not be a recreational activity: it is a simplified model of interdependent choices.

Game theorists distinguish models in several ways. Cooperative games allow binding agreements, while non-cooperative analysis focuses on situations where such agreements are unavailable. Other distinctions concern whether players choose at the same time or in sequence, and whether they have complete or incomplete information. A solution concept is a rule for identifying or predicting a strategy profile or outcome in a game. In a Nash equilibrium, each player's strategy is a best response to the strategies of the others: no player can improve their payoff by changing their own strategy alone while the others keep theirs unchanged.

An equilibrium is conditional on the players, options, information and payoffs represented in a model. It does not, by itself, establish that an outcome is fair, efficient or best for everyone. The Prisoner's Dilemma is a classic illustration: for its specified incentives, each of two players has reason to choose a strategy that leads to a Nash equilibrium, even though both would receive a better payoff if they could bind themselves to cooperate. The example helps explain why individually sensible choices can produce a collectively worse result, and why changing communication, commitments or incentives can change the analysis.

Game theory's modern mathematical framework grew from work by mathematician John von Neumann and economist Oskar Morgenstern. John Nash developed a widely used equilibrium concept for non-cooperative games; later work by Reinhard Selten and John Harsanyi extended equilibrium analysis to dynamic situations and games with incomplete information. The framework is used to examine strategic problems in economics and political science, and to model interactions in biology. Its usefulness depends on how well a model captures the relevant choices and incentives; it complements rather than replaces evidence about real behaviour.