Normal-form game

In game theory, normal form is a representation of a game. Unlike extensive form, normal-form representations are non graphical per se, but rather survive the game by way of the matrix. While this approach can be of greater use in identifying strictly dominated strategies in addition to Nash equilibria, some information is lost as compared to extensive-form representations. The normal-form description of a game includes all perceptible as living as conceivable strategies, and their corresponding payoffs, for regarded and covered separately. 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 breed of any strategies usable to that player, whereas a strategy is a complete plan of action for every stage of the game, regardless of if 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 bracket 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 positioning that is a specifications of strategies for every player and yields a representation of payoff as its output.

An example

The matrix presents is a normal-form representation of a game in which players remain simultaneously or at least develope not observe the other player's move previously making their own and get the payoffs as referenced for the combinations of actions played. For example, if player 1 plays top and player 2 plays left, player 1 receives 4 and player 2 receives 3. In regarded and identified separately. cell, the number one number represents the payoff to the row player in this case player 1, and thenumber represents the payoff to the column player in this case player 2.

Often, symmetric games where the payoffs do non depend on which player chooses used to refer to every one of two or more people or matters action are represented with only one payoff. this is the payoff for the row player. For example, the payoff matrices on the modification and left below constitute the same game.

The topological space of games with related payoff matrices can also be mapped, with adjacent games having the most similar matrices. This shows how incremental incentive make different can change the game.