Zero-Sum Game - Definition

A zero sum game is a term used in Game theory to describe both real games, and situations of all kinds, usually between two players or participants, where the gain of one player is offset by the loss of another player, equalling the sum of zero. For instance, if you play a single game of chess with someone, one person will lose and one person will win. The win (+1) added to the loss (-1) equals zero. In contrast, non-zero-sum describes a situation in which the interacting parties' Aggregate gains and losses are either less than or more than zero. A zero-sum game is also called a strictly competitive game. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash Equilibrium.

If you play chess in a tournament, each individual match is zero sum, with one winner and one loser. However, outside of the game, you are given a number ranking. This ranking can change significantly if you lose to someone of a much lower rank. It may not alter much if you lose to a much higher-ranking player. When a single game is actually one in a series with an outside ranking, the total result may be non zero sum, since wins or losses are not the only thing that count.

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