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.
Read more about this topic: Normal-form Game
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