In this paper we formalize a new form of two-player game, that we call decision- form. A two-player decision-form game consists in a pair of decision rules, representing the rationality of each player. We develop the basic facts of this type of games, showing that this form of game generalizes the normal-form . Indeed, we show that with a normal form game it is possible, in a natural way, to associate a decision form game. In the paper we give examples of decision-form games not-deriving, a priori, by normal-form games. We observe that it is possible to associate with a normal-form game several decision-form games, each representing a possible decisional behavior of the pair of players. The classic best-response behavior is only one of these possible behaviors.