In
game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
, 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 game A two-player game is a multiplayer game that is played by precisely two players. This is distinct from a solitaire game, which is played by only one player.
Examples
The following are some examples of two-player games. This list is not intended ...
s that are only specified for two players. In defining ''n''-player games,
game theorist
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
s usually provide a definition that allow for any (finite) number of players.
The limiting case of
is the subject of
mean field game theory Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. It lies at the intersection of game theory with stochastic analysis and control theory. The use of the term "mean field" is insp ...
.
Changing games from 2-player games to ''n''-player games entails some concerns. For instance, the
Prisoner's dilemma
The Prisoner's Dilemma is an example of a game analyzed in game theory. It is also a thought experiment that challenges two completely rational agents to a dilemma: cooperate with their partner for mutual reward, or betray their partner ("defe ...
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
In game theory, the unscrupulous diner's dilemma (or just diner's dilemma) is an ''n''-player prisoner's dilemma. The situation imagined is that several people go out to eat, and before ordering, they agree to split the cost equally between them. ...
.)
References
Game theory game classes
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