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In game theory and economic theory, a zero – sum game is a mathematical representation of a situation in which a participant's gain ( or loss ) of utility is exactly balanced by the losses ( or gains ) of the utility of the other participant ( s ).

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 larger piece reduces the amount of cake available for others, is a zero – sum game if all participants value each unit of cake equally ( see marginal utility ).

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 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.