  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 the author
and already studied and applied to economic games). In the work we define the
concept of super-reactivity, the preorder of re-activity 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, with respect to the pair
of best reply decision rules, and dominance (with respect to the payoff
functions of the game) is completely revealed.
