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In [[game theory]], '''normal form''' is a description of a '''game''' using a [[Matrix (mathematics)|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 ==

* [[Game theory]]
* [[Matrix (mathematics)]]

== External links ==

* [https://en.wikipedia.org/wiki/Normal-form_game Normal-form game] @ Wikipedia


[[Category:Game theory]]