Game theory -- the abstract study of games, or the mathematics of competition and cooperation -- analyzes situations in terms of gains and losses of opposing players. Two major theories about modern life have come out of games. The first is probability theory, which was first developed out of games of chance in the 17th century by Blaise Pascal. The strategies used to achieve success on the game board can also be applied in many real-life situations.

Game theory is a system for predicting how people should optimally behave in situations of conflict. In a typical game, decision-making "players," who each have their own goals, try to outsmart one another by anticipating each other's decisions; the game is resolved as a consequence of the players' decisions. A solution to a game prescribes the decisions the players should make and describes the game's appropriate outcome.

It is applied widely in economics, operations research, military and political science, organization theory, the study of negotiation, warfare, economic competition, to determine the formation of political coalitions or business conglomerates, the optimum price at which to sell products or services, the power of a voter or a bloc of voters, the selection of a jury, the best site for a manufacturing plant, and even the behaviour of certain species in the struggle for survival.

Game theory was developed out of games of strategy in the 1920s by mathematician John von Neumann and Oskar Morgenstern. It did't become well known until the publication in 1944 of their Theory of Games and Economic Behavior.

Its importance in economic theory, for example, was shown by the awarding of the 1993/4 Nobel Prize for economics to three prominent game-theoreticians: American mathematician John F. Nash, Hungarian-American economist John C. Harsanyi, and German economist Reinhard Selten. Nash's contribution was the development of an idea now known as the Nash Equilibrium, a key component in the study of game theory.

The Minimax Theorem discovered by von Neumann in 1928 asserts that every finite, zero-sum, two-player game has a minimax value if mixed strategies are allowed. This means that every such game has a solution (an optimal strategy) -- but it may be hard to find the solution. Zero-sum means that any gain for one player represents an equal loss for the other. Many parlor games are zero-sum, but the "games" found in economics or in operations research usually are not, since wealth may be created or destroyed.

The Minimax Theorem does't apply to nonzero-sum games or games with more than two players. John Nash showed in 1950 that such games do have a weaker solution, a noncooperative equilibrium in which no player, acting on the assumption that the other players' strategies are fixed, can gain anything by changing his or her own strategy. These solutions are often called Nash equilibria.