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 ${\displaystyle n\to \infty }$ 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.)

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^n, are required for traversing the game tree to optimize the score for a specific player.[3]

References

1. Binmore, Ken (2007). Playing for Real : A Text on Game Theory:. Oxford University Press. p. 522. ISBN 9780198041146.
2. 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.
3. Luckhardt, Carol A.; Irani, Keki B. (11 August 1986). An Algorithmic Solution of N-Person Games (PDF). AAAI '86. pp. 158–162. Archived (PDF) from the original on 19 April 2024. Retrieved 20 August 2024.