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Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."〔Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p. (1 ). Chapter-preview links, pp. (vii–xi ).〕 Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, and biology. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by the 1944 book ''Theory of Games and Economic Behavior'', co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty. This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. With the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole in 2014, eleven game-theorists have now won the economics Nobel Prize. John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology. ==Representation of games== The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the ''players'' of the game, the ''information'' and ''actions'' available to each player at each decision point, and the ''payoffs'' for each outcome. (Rasmusen refers to these four "essential elements" by the acronym "PAPI".)〔 A game theorist typically uses these elements, along with a solution concept of their choosing, to deduce a set of equilibrium strategies for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Game theory」の詳細全文を読む スポンサード リンク
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