Game Theory
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Abstract
numerical payons can be assigned. Games such as chess and poker, together with many social, economic, political and military conflicts which are not commonly thought of as games, possess these properties and are therefore amenable in principle to game theory analysis. The primary goal of the theory is to determine, through formal reasoning alone, what strategies the players ought to choose in order to pursue their interests rationally, and what outcomes will result if they Although some Zermelo in 1912, and by the theory was not firmly von Neumann proved the fumlamclllal theorem in 1928. This theorem strictly competitive (zero-sum) payoffs are simply the negatives of the other player's. If the number of strategies is finite, and the players are permitted to use randomizing devices to 'choose' weighted averages of their strategies, then each player can adopt a strategy that yields the best payoff givcn the most damaging counter-strategies available to the adversary. The minimax theorem asserts that these payoffs are equal, and that every game of this type therefore has a well-defined the paradoxical property that whereas each player has a domirwnt strategy that yields the best payoff against both of the opponent's available counter-strategies, each player obtains a better payoff if both chouse dominated strategies. generalization of thi~, the N-Perso/l discovered in the early 1970s; player is better off if all choose if all choose domiPrisoners' Dilemma is a problems, including resource environmental pollution, and arms races. Experimental games have been used by psychologists to study co-operation and competition in twoperson and multi-person groups, and economists have applied game theory to the study of bargaining and collective choice. In political science and sociology, game theory has been used to analyse voting behaviour and coalition formation, and numerous other applications social anthropology and other aucmpted. During the 1970s, applicat ions to the study of the evolution began to flourish in sociobiology.