Lexicographic agreeing to disagree and perfect equilibrium

Bach, C. W. ORCID: https://orcid.org/0000-0003-0187-1820 and Cabessa, J. (2023) Lexicographic agreeing to disagree and perfect equilibrium. Journal of Mathematical Economics, 109. 102908. ISSN 03044068 doi: 10.1016/j.jmateco.2023.102908

Abstract/Summary

Aumann’s seminal agreement theorem deals with the impossibility for agents to acknowledge their distinct posterior beliefs. We consider agreeing to disagree in an extended framework with lexicographic probability systems. A weak agreement theorem in the sense of identical posteriors only at the first lexicographic level obtains. Somewhat surprisingly, a possibility result does emerge for the deeper levels. Agents can agree to disagree on their posteriors beyond the first lexicographic level. By means of mutual absolute continuity as an additional assumption, a strong agreement theorem with equal posteriors at every lexicographic level ensues. Subsequently, we turn to games and provide epistemic conditions for the classical solution concept of perfect equilibrium. Our lexicographic agreement theorems turn out to be pivotal in this endeavour. The hypotheses of mutual primary belief in caution, mutual primary belief in rationality, and common knowledge of conjectures characterize perfect equilibrium epistemically in our lexicographic framework.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/118767
Identification Number/DOI	10.1016/j.jmateco.2023.102908
Refereed	Yes
Divisions	Arts, Humanities and Social Science > School of Politics, Economics and International Relations > Economics
Publisher	Elsevier
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