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In general, a game is a way of describing a situation in which players make choices with the intent of optimizing their utility. Formally, a game includes three features:

a set of pure strategies for each player (their strategy space)

a way of determining an outcome from the strategies selected by the players

a utility function for each player specifying their payoff for each outcome
Defines:
outcome, game, player, utility function, payoff
Related:
CommonKnowledge, NormalFormGame, CompleteInformation, Strategy2
Type of Math Object:
Definition
Major Section:
Reference
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