Normal-form game
In game theory, normal form is a description of a game using a matrix.
Description
The normal-form representation of a game includes all perceptible and conceivable strategies, and their corresponding payoffs, for 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, whereas 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.
Extensive-form representations
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.
See also
External links
- Normal-form game @ Wikipedia
