Qualitative analysis of common belief of rationality in strategic-form games

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