Zero–sum Game

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.