constant-sum game

game theory

Also known as: zero-sum game

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Last updated

July 23, 2026

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In game theory, a constant-sum game is a situation where the total gains and losses for all players add up to zero. This means that any advantage one player gains is directly at the expense of another player. These games are also known as zero-sum games.12

Examples of constant-sum games include chess, checkers, and Go, which are games of perfect information. In these games, players can use all available information to deduce optimal strategies, leading to a predetermined outcome. However, in situations without a clear "saddlepoint" (a best strategy for all players), game theory prescribes using mixed strategies, which involve choosing actions based on probability distributions. The minimax theorem states that every finite, two-person constant-sum game has a solution, either in pure or mixed strategies.34

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game theory
Classification of games
Constant-sum games are games of total conflict, which are also called games of pure competition. Poker, for example, is a constant-sum game because the combined wealth of the players remains constant, though its distribution shifts in the course of play.
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Constant-sum games are games of total conflict, which are also called games of pure competition. Poker, for example, is a constant-sum game because the combined wealth of the players remains constant, though its distribution shifts in the course of play.
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positive-sum game
…the positive-sum game are the zero-sum game and the negative-sum game. The term zero-sum game refers to situations in which the total of wins and losses adds up to zero, and thus one party benefits at the direct expense of another. The term negative-sum game describes situations in which the…
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…the positive-sum game are the zero-sum game and the negative-sum game. The term zero-sum game refers to situations in which the total of wins and losses adds up to zero, and thus one party benefits at the direct expense of another. The term negative-sum game describes situations in which the…
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war
Diplomacy
…theorists distinguish antagonistic situations called zero-sum games, in which one state’s gain can be only at the expense of another state because the “payoff” is fixed. Even then a mutually acceptable distribution of gains can be rationally reached on the basis of the “minimax” principle—the party in a position of…
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…theorists distinguish antagonistic situations called zero-sum games, in which one state’s gain can be only at the expense of another state because the “payoff” is fixed. Even then a mutually acceptable distribution of gains can be rationally reached on the basis of the “minimax” principle—the party in a position of…
Read More