Reactivity (in decision-form games)

In this paper we introduce the reactivity in decision-form games. The concept of reactivity allows us to give a natural concept of rationalizable solution for decision-form games: the solubility by elimination of sub-reactive strategies. This concept of solubility is less demanding than the concept of solubility by elimination of non-reactive strategies (introduced by D. Carfì and already studied and applied to economic games). In the work we define the concept of super-reactivity, the preorder of reactivity and, after a characterization of super-reactivity, we are induced to give the concepts of maximal-reactivity and sub-reactivity; the latter definition permits to introduce the iterated elimination of sub-reactive strategies and the solubility of a decision-form game by iterated elimination of sub-reactive strategies. In the paper several examples are developed. Moreover, in the case of normal-form games, the relation between reactivity and dominance is completely revealed.