N-player game explained

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

n \to inf ty 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 sucker's payoff. (One example of an n-player Prisoner's Dilemma is the Diner's dilemma.)

Notes and References

1. Book: Binmore, Ken. Playing for Real : A Text on Game Theory:. 2007. Oxford University Press. 9780198041146. 522.
2. Markus . Fischer . On the connection between symmetric N-player games and mean field games . Annals of Applied Probability . 27 . 2 . 2017 . 757-810 . 10.1214/16-AAP1215 . 1405.1345 .