Qualitative Analysis of Common Belief of Rationality in Strategic-Form Games

Abstract

In this paper we study common belief of rationality in strategic-form games with ordinal utilities, employing a qualitative doxastic model of beliefs. We characterize the three main solution concepts for such games, viz., Iterated Deletion of Strictly Dominated Strategies (IDSDS), Iterated Deletion of Borgers-dominated Strategies (IDBS) and Iterated Deletion of Inferior Strategy Profiles (IDIP), by means of gradually restrictive properties imposed on the doxastic models. As a corollary, we prove that IDIP refines IDBS, which refines IDSDS.

Keywords: Common belief of rationality, Qualitative beliefs, Ordinal utilities, Iterated Deletion of Strictly Dominated Strategies, Iterated deletion of Borgers-dominated strategies, Iterated deletion of inferior profiles

JEL Classification: C72, D81, D83