Reactivity in decision-form games

Carfì, David (2009): Reactivity in decision-form games.

Abstract

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 elimina- tion of sub-reactive strategies. In the paper several examples are devel- oped. Moreover, in the case of normal-form games, the relation between reactivity and dominance is completely revealed.

• Item Type: MPRA Paper
• Language: English
• Keywords: Decision form games; reactivity; dominance
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C79 - Other; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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