# Zero-sum game

## Situation where total gains match total losses / From Wikipedia, the free encyclopedia

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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]} 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.^{[2]}

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, and bridge where one person gains and another person loses, which results in a zero-net benefit for every player.^{[3]} In the markets and financial instruments, futures contracts and options are zero-sum games as well.^{[4]}

In contrast, **non-zero-sum** describes a situation in which the interacting parties' aggregate gains and losses can be less than or more than zero. 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,^{[5]} or with Nash equilibrium. Prisoner's Dilemma is a classic non-zero-sum game.^{[6]}