Normal-form Game - General Formulation

General Formulation

In order for a game to be in normal form, we are provided with the following data:

• There is a finite set P of players, which we label {1, 2, ..., m}

• Each player k in P has a finite number of pure strategies

A pure strategy profile is an association of strategies to players, that is an m-tuple

such that

A payoff function is a function

whose intended interpretation is the award given to a single player at the outcome of the game. Accordingly, to completely specify a game, the payoff function has to be specified for each player in the player set P= {1, 2, ..., m}.

Definition: A game in normal form is a structure

where:

is a set of players,

is an m-tuple of pure strategy sets, one for each player, and

is an m-tuple of payoff functions.