{{Short description|Game which can have any number of players}} {{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.<ref name=Binmore>{{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}}</ref> The limiting case of <math>n \to \infty</math> is the subject of mean field game theory.<ref>{{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 }}</ref>
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.)
==Analysis==
''n''-player games can not be solved using minimax, the theorem that is the basis of tree searching for ''2''-player games. Other algorithms, like max<sup>n</sup>, are required for traversing the game tree to optimize the score for a specific player.<ref>{{cite conference |last1=Luckhardt |first1=Carol A. |last2=Irani |first2=Keki B. |title=An Algorithmic Solution of N-Person Games |date=11 August 1986 |conference=AAAI '86 |pages=158–162 |url=https://cdn.aaai.org/AAAI/1986/AAAI86-025.pdf |access-date=20 August 2024 |archive-date=19 April 2024 |archive-url=https://web.archive.org/web/20240419091220/https://cdn.aaai.org/AAAI/1986/AAAI86-025.pdf |url-status=live }}</ref>
==References== {{reflist}}
{{Game theory}}
Category:Game theory game classes
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