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# GAME THEORY

Game theory is a branch of mathematical analysis developed to study decision making in conflict situations. Such a situation exists when two or more decision makers who have different objectives act on the same system or share the same resources. There are two person and multiperson games. Game theory provides a mathematical process for selecting an OPTIMUM STRATEGY (that is, an optimum decision or a sequence of decisions) in the face of an opponent who has a strategy of his own.

In game theory one usually makes the following assumptions:

(1) Each decision maker ["PLAYER"] has available to him two or more well-specified choices or sequences of choices (called "PLAYS").

(2) Every possible combination of plays available to the players leads to a well-defined end-state (win, loss, or draw) that terminates the game.

(3) A specified payoff for each player is associated with each end-state (a [ZERO-SUM game] means that the sum of payoffs to all players is zero in each end-state).

(4) Each decision maker has perfect knowledge of the game and of his opposition; that is, he knows in full detail the rules of the game as well as the payoffs of all other players.

(5) All decision makers are rational; that is, each player, given two alternatives, will select the one that yields him the greater payoff.

The last two assumptions, in particular, restrict the application of game theory in real-world conflict situations. Nonetheless, game theory has provided a means for analyzing many problems of interest in economics, management science, and other fields. (IIASA)

A general theory of rational behavior for situations in which (1) two (two-person games) or more (multi-person games) decision makers (players) have available to them (2) a finite number of courses of action (plays) each leading to (3) a well defined outcome or end with gains and losses expressed in terms of numerical payoffs associated with each combination of courses of action and for each decision maker. The decision makers have (4) perfect knowledge of the rules of the game, i.e., (1), (2) and (3) but no knowledge about the opponents' moves and are (5) rational in the sense of making decisions that optimize their individual gains. The matrix of payoffs can represent various conflicts. In a zero-sum game one person wins what the other loses. In other situations gains and losses may be unequally distributed which allows the representation of numerous competitive and conflict situations. The theory proposes several solutions, e.g., in a minimax strategy each participants minimizes the maximum loss the other can impose on him, a mixed strategy involves probabilistic choices. Experiments with such games revealed conditions for cooperation, defection and the persistence of conflict. The theory and some of the results have found applications in economics, management science bargaining and conflict resolution among many areas of interest. (Krippendorff)
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