Definition:Zero-Sum Game

Definition

A zero-sum game is a game in which the total of the payoffs to all players is zero.

Non-Zero-Sum Game

A non-zero-sum game is a game in which the total of the payoffs to all players is dependent upon the moves made to reach those payoffs.

Examples

Chess

Let two players of chess decide that the loser shall play the winner a fixed sum of money.

This is then an example of a zero-sum game.

Poker

An example of a zero-sum game is the game of poker:

the total amount of money on the table is fixed, and what one person loses the other players win.

Also known as

A zero-sum game is also known as a constant sum game.

Also see

• Results about zero-sum games can be found here.

Sources

• 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $2$
• 1983: Morton D. Davis: Game Theory (revised ed.) ... (previous) ... (next): $\S 2$: The Two-Person, Zero-Sum Game with Equilibrium Points
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): zero-sum game
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): game theory
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): zero-sum game
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): game theory
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): zero-sum game
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): zero-sum game
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): zero-sum game