game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

, 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. The limiting case of

n \to \infty

is the subject of

mean field game theory Mean-field game theory is the study of strategic decision making by small interacting agent (economics), agents in very large populations. It lies at the intersection of game theory with stochastic analysis and control theory. The use of the term " ...

. Changing games from 2-player games to ''n''-player games entails some concerns. For instance, the

Prisoner's dilemma The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ("defect") for individual gain. The dilemma arises from the fact that while def ...

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 Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss function, loss for a Worst-case scenari ...

, the theorem that is the basis of tree searching for ''2''-player games. Other algorithms, like maxⁿ, are required for traversing the game tree to optimize the score for a specific player.

References

Game theory game classes {{gametheory-stub