*n*-player game

In game theory, an ** n-player game** is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players. In defining

*n*-player games, game theorists usually provide a definition that allow for any (finite) number of players.

^{[1]}The limiting case of is the subject of mean field game theory.

^{[2]}

Changing games from 2-player games to *n*-player games entails some concerns. For instance, the Prisoner's dilemma is a 2-player game. One might define an *n*-player Prisoner's Dilemma where a single defection results everyone else getting the sucker's payoff. Alternatively, it might take certain amount of defection before the cooperators receive the suckers payoff. (One example of an *n*-player Prisoner's Dilemma is the Diner's dilemma.)

## References[edit]

**^**Binmore, Ken (2007).*Playing for Real : A Text on Game Theory:*. Oxford University Press. p. 522. ISBN 9780198041146.**^**Fischer, Markus (2017). "On the connection between symmetric*N*-player games and mean field games".*Annals of Applied Probability*.**27**(2): 757–810. arXiv:1405.1345. doi:10.1214/16-AAP1215.

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