Reactivity in decision-form games

TL;DR

This paper introduces reactivity in decision-form games, providing a new rationalizability concept via elimination of sub-reactive strategies, and explores its properties and relation to dominance in normal-form games.

Contribution

It defines reactivity, super-reactivity, and related concepts, and develops a framework for solving decision-form games through iterative elimination of sub-reactive strategies.

Findings

Reactivity offers a natural rationalizability concept.

Iterated elimination of sub-reactive strategies solves certain games.

Reactivity relates to dominance in normal-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 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.