Game theory

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Game theory is a method for exploring the predicted and actual behavior of individuals in interactions with formalized incentive structures. Seemingly different types of interactions can be characterized as having similar incentive structures, thus being examples of a particular "game."

Though touched on by earlier mathematical results, modern game theory became a prominent branch of mathematics in the 1940s, especially after the 1944 publication of The Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. Game theory differs from the related field of economics in that it seeks to find rational strategies in situations where the outcome depends not only on one's own strategy and "market conditions", but upon the strategies chosen by other players with possibly different or overlapping goals. For this reason, it is also commonly used in political science.

As with economics, the results can be applied to simple games of entertainment or to more significant aspects of life and society. An example of the latter is the prisoner's dilemma as popularized by mathematician Albert W. Tucker, which has many implications about the nature of human cooperation. Biologists have used game theory to understand and predict certain outcomes of evolution, such as the concept of evolutionarily stable strategy introduced by John Maynard Smith in his essay Game Theory and the Evolution of Fighting. See also Maynard Smith's book Evolution and the Theory of Games.

Game theory classifies games into many categories that determine which particular methods can be applied to solving them (and indeed how one defines "solved" for a particular category). Some common categories are:

  • Zero-sum games are those in which the total benefit to all players in the game must add to zero (or more informally put, that each player benefits only at the expense of another). Chess and Poker are zero-sum games, because one wins exactly the amount one's opponents lose. Business and politics, for example, are nonzero-sum games because some outcomes are good for all players or bad for all players.
  • Cooperative games are those in which the players may freely communicate among themselves before making game decisions and may make bargains to influence those decisions.
  • Complete information games are those in which each player has the same game-relevant information as every other player. Chess is a complete-information game, while Poker is not.

Other branches of mathematics, in particular probability and statistics, are commonly used in conjuction with game theory to analyse many games.

See also Mathematical games

Further Reading:

  • Oskar Morgenstern, John von Neumann: The Theory of Games and Economic Behavior, 3rd ed., Princeton University Press 1953
  • Mike Shor: Game Theory .net, Lecture notes, interactive illustrations and other information.
  • Maynard Smith: Evolution and the Theory of Games, Cambridge University Press 1982

A version of this page has been translated into Portuguese.