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A multiplayer game has several players, who may be independent opponents or teams. Games with many independent players are difficult to analyse formally using game theory as the players may form coalitions. The term "game" in this context may mean either a true game played for entertainment, or a competitive activity describable in principle by mathematical game theory.
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Game theory
John Nash proved that games with several players have a stable solution provided that coalitions between players are not allowed. He won the Nobel prize for economics for this important result which extended von Neumann's theory of zero-sum games. Such a stable strategy is called a Nash equilibrium.
If cooperation between players is allowed, then the game is more complex. Many concepts have been developed to analyze such games. While these have had some partial success in the fields of economics, politics and conflict, no good general theory has yet been developed.
In quantum game theory, it has been found that the introduction of quantum information into multiplayer games allows a new type of equilibrium strategy which is not found in traditional games. The entanglement of players's choices can have the effect of a contract by preventing players from profiting from betrayal.
Types
Examples of multiplayer games for entertainment include: