Zero-sum game
mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants
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. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.
If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, sport and bridge where one person gains and another person loses, which results in a zero-net benefit for every player. In the markets and financial instruments, futures contracts and options are zero-sum games as well.
A zero-sum game is also called a strictly competitive game, while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium.
In contrast, positive-sum or win–win games describe a situation in which the interacting parties' aggregate gains and losses can be more than zero. Prisoner's Dilemma is a classic non-zero-sum game.
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The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated May 28, 2026. The linked authority identifier is Q156612. The Library of Congress control number is sh95004000. 1 of 1 selected statements include explicit references; 1 carry qualifiers and 0 use preferred rank.
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This entry incorporates text from “Zero-sum game” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.