Generally, any game where all strategies are Pareto optimal is called a conflict game. The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is Pareto optimal. Definition Īnother example of the classic zero-sum game Prisoner's Dilemma is a classic non-zero-sum game. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium. A zero-sum game is also called a strictly competitive game, while non-zero-sum games can be either competitive or non-competitive.

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. In the markets and financial instruments, futures contracts and options are zero-sum games as well. 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. 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. If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.

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. Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two sides, where the result is an advantage for one side and an equivalent loss for the other. For other uses, see Zero sum (disambiguation).

Null vector game