Normal-form 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, for each player.

The matrix provided is a normal-form representation of a game in which players move simultaneously (or at least do not observe the other player's move before making their own) and receive the payoffs as specified for the combinations of actions played.

The payoff matrix facilitates elimination of dominated strategies, and it is usually used to illustrate this concept.

These matrices only represent games in which moves are simultaneous (or, more generally, information is imperfect).

Definition: A game in normal form is a structure where: is a set of players, is an I-tuple of pure strategy sets, one for each player, and is an I-tuple of payoff functions.

A partial topology of two-player, two-strategy games, including such games as Prisoner's dilemma , Stag hunt , and Chicken
Both extensive and normal-form illustration of a sequential game with subgame imperfect and perfect Nash equilibria marked with red and blue respectively.