Normal-form Game
In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent the game by way of a matrix. While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria, some information is lost as compared to extensive-form representations. The normal-form representation of a game includes all perceptible and conceivable strategies, and their corresponding payoffs, of each player.
In static games of complete, perfect information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is the set of all strategies available to that player, where a strategy is a complete plan of action for every stage of the game, regardless of whether that stage actually arises in play. A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a strategy profile (that is a specification of strategies for every player) and yields a representation of payoff as its output.
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Famous quotes containing the word game:
“My first big mistake was made when, in a moment of weakness, I consented to learn the game; for a man who can frankly say “I do not play bridge” is allowed to go over in the corner and run the pianola by himself, while the poor neophyte, no matter how much he may protest that he isn’t “at all a good player, in fact I’m perfectly rotten,” is never believed, but dragged into a game where it is discovered, too late, that he spoke the truth.”
—Robert Benchley (1889–1945)