Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2011-03-04
Nonlinear Sciences
Adaptation and Self-Organizing Systems
20 pages
Scientific paper
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.
Carfí David
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