A branch of applied mathematics that studies strategic situations in which individuals or organisations choose various actions in an attempt to maximize their returns
The study of decision problems in competitive situations Game theory is the procedure for analyzing and deriving rules for making decisions when two or more people or organizations are competing for some objective
(l) The study of situations involving competing interests, modeled in terms of the strategies, probabilities, actions, gains, and losses of opposing players in a game See also management game; war game (2) The study of games to determine the probability of winning, given various strategies
A mathematical method of decision-making in which a competitive situation is analyzed to determine the optimal course of action for an interested party, often used in political, economic, and military planning. Also called theory of games. Branch of applied mathematics devised to analyze certain situations in which there is an interplay between parties that may have similar, opposed, or mixed interests. Game theory was originally developed by John von Neumann and Oscar Morgenstern in their book The Theory of Games and Economic Behavior (1944). In a typical game, or competition with fixed rules, "players" try to outsmart one another by anticipating the others' decisions, or moves. A solution to a game prescribes the optimal strategy or strategies for each player and predicts the average, or expected, outcome. Until a highly contrived counterexample was devised in 1967, it was thought that every contest had at least one solution. See also decision theory; prisoner's dilemma
theory designed to understand strategic choices, that is, to understand how people or organizations behave when they expect their actions to influence the behavior of others
The study of the ways in which player's preferences and strategic interactions among rational players produces game outcomes, with emphasis on outcomes that were not intended by any of the players
a branch of applied mathematics with many uses in economics, including the analysis of the interaction of firms that take each others actions into account (chapter 11)
In general, a (mathematical) game can be played by one player, such as a puzzle, but its main connection with mathematical programming is when there are at least two players, and they are in conflict Each player chooses a strategy that maximizes his payoff When there are exactly two players and one player's loss is the other's gain, the game is called zero sum In this case, a payoff matrix, A, is given where Aij is the payoff to player 1, and the loss to player 2, when player 1 uses strategy i and player 2 uses strategy j In this representation each row of A corresponds to a strategy of player 1, and each column corresponds to a strategy of player 2 If A is m × n, this means player 1 has m strategies, and player 2 has n strategies Here is an example of a 2 × 3 payoff matrix
A field of study that bridges mathematics, statistics, economics, and psychology It is used to study economic behavior, and to model conflict between nations, for example, "nuclear stalemate" during the Cold War