Rules generally determine the time-keeping system, the rights and responsibilities of the players, and each player’s goals. Player rights may include when they may spend resources or move tokens.
A multiplayer game is a game of several players who may be independent opponents or teams. Games with many independent players are difficult to analyze formally using game theory as the players may form and switch 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.
John Nash proved that games with several players have a stable solution provided that coalitions between players are disallowed. Nash won the Nobel prize for economics for this important result which extended von Neumann’s theory of zero-sum games. Nash’s stable solution is known as the Nash equilibrium.
If cooperation between players is allowed, then the game becomes 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 not found in traditional games. The entanglement of players’s choices can have the effect of a contract by preventing players from profiting from what is known as betrayal.