In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each 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 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, or with Nash equilibrium.

Definition

The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is Pareto optimal (generally, any game where all strategies are Pareto optimal is called a conflict game).

Zero sum is a situation in which a participant's gain or loss is exactly balanced by the losses or gains of the other participants.

Zero sum may also refer to:

See also

"Zero Sum" is the twenty-first episode of the fourth season of the American science fiction television series The X-Files. It premiered on the Fox network on April 27, 1997. It was directed by Kim Manners, and written by Frank Spotnitz and Howard Gordon. "Zero Sum" included appearances by William B. Davis, Laurie Holden and Morris Panych. The episode helped to explore the overarching mythology, or fictional history of The X-Files. "Zero Sum" earned a Nielsen household rating of 11.7, being watched by 18.6 million people in its initial broadcast. The episode has received mixed to positive responses from critics.

The show centers on FBI special agents Fox Mulder (David Duchovny) and Dana Scully (Gillian Anderson) who work on cases linked to the paranormal, called X-Files. In the episode, a case Mulder is asked to investigate is covertly covered up by the agents' boss Walter Skinner (Mitch Pileggi), who has made a sinister bargain with The Smoking Man (Davis).

The decision to center another episode around Skinner—following the third season episode "Avatar"—was made when Gillian Anderson took a week off to shoot the film The Mighty. Rather than have Duchovny carry the additional workload, the writing staff decided to focus the episode on supporting cast members. "Zero Sum" was the final appearance in the series by Morris Panych. In addition, the episode saw the return of the virus-carrying bees from the season-opener "Herrenvolk" and would later return in the 1998 feature film.