n-player game

{{DISPLAYTITLE: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.{{cite book|last=Binmore|first=Ken|title=Playing for Real : A Text on Game Theory:|year=2007|publisher=Oxford University Press|isbn=9780198041146|page=522}} The limiting case of $n\; \backslash to\; \backslash infty$ is the subject of mean field game theory.{{cite journal |first=Markus |last=Fischer |title=On the connection between symmetric N-player games and mean field games |journal=Annals of Applied Probability |volume=27 |issue=2 |year=2017 |pages=757-810 |doi=10.1214/16-AAP1215 |arxiv=1405.1345 }}

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.)