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

22 Pages Posted: 12 May 2017 Last revised: 12 Oct 2017

See all articles by Giacomo Bonanno

Giacomo Bonanno

University of California, Davis - Department of Economics

Elias Tsakas

Maastricht University - Department of Economics

Date Written: October 3, 2017

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

Suggested Citation

Bonanno, Giacomo F. and Tsakas, Elias, Qualitative Analysis of Common Belief of Rationality in Strategic-Form Games (October 3, 2017). Available at SSRN: https://ssrn.com/abstract=2967471 or http://dx.doi.org/10.2139/ssrn.2967471

Giacomo F. Bonanno

University of California, Davis - Department of Economics ( email )

One Shields Drive
Davis, CA 95616-8578
United States
916-752-1574 (Phone)
916-752-9382 (Fax)

Elias Tsakas (Contact Author)

Maastricht University - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

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