The reduction of qualitative games

TL;DR

This paper extends the concept of iterated elimination of strictly dominated strategies to qualitative games, establishing conditions for unique, nonempty maximal reductions and generalizing previous results in game theory.

Contribution

It introduces new dominance relations and reduction methods for qualitative games, broadening the applicability of IESDS beyond Nash strategic games.

Findings

Existence of unique, nonempty maximal reductions under certain conditions

Generalization of results by Dufwenberg and Stegeman (2002) and Apt (2007)

Development of several types of dominance relations for qualitative games

Abstract

We extend the study of the iterated elimination of strictly dominated strategies (IESDS) from Nash strategic games to a class of qualitative games. Also in this case, the IESDS process leads us to a kind of 'rationalizable' result. We define several types of dominance relation and game reduction and establish conditions under which a unique and nonempty maximal reduction exists. We generalize, in this way, some results due to Dufwenberg and Stegeman (2002) and Apt (2007).