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

Examples of zero-sum game include:

• Poker: the total amount of money on the table is fixed -- 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): zero-sum game
• 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