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Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. [1]
Nash proved that every finite n-player, non-zero-sum (not just two-player zero-sum) non-cooperative game has what is now known as a Nash equilibrium in mixed strategies. Game theory experienced a flurry of activity in the 1950s, during which the concepts of the core , the extensive form game , fictitious play , repeated games , and the Shapley ...
The concept of a mixed-strategy equilibrium was introduced by John von Neumann and Oskar Morgenstern in their 1944 book The Theory of Games and Economic Behavior, but their analysis was restricted to the special case of zero-sum games. They showed that a mixed-strategy Nash equilibrium will exist for any zero-sum game with a finite set of ...
Matching Pennies is a zero-sum game because each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the participants' total gains are added up and their total losses subtracted, the sum will be zero.
Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
Zero-sum thinking perceives situations as zero-sum games, where one person's gain would be another's loss. [1] [2] [3] The term is derived from game theory. However, unlike the game theory concept, zero-sum thinking refers to a psychological construct—a person's subjective interpretation of a situation. Zero-sum thinking is captured by the ...
The first theorem in this sense is von Neumann's minimax theorem about two-player zero-sum games published in 1928, [2] which is considered the starting point of game theory. Von Neumann is quoted as saying "As far as I can see, there could be no theory of games
Minimax is used in zero-sum games to denote minimizing the opponent's maximum payoff. In a zero-sum game, this is identical to minimizing one's own maximum loss, and to maximizing one's own minimum gain. "Maximin" is a term commonly used for non-zero-sum games to describe the strategy which maximizes one's own minimum payoff.