 Lexicographic agreeing to disagree and perfect equilibriumChristian W. Bach and Jérémie Cabessa Journal of Mathematical Economics, 2023, vol. 109, issue C Abstract: 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. Keywords: Agreeing to disagree; Lexicographic probability systems; Epistemic game theory; Mutual absolute continuity; Perfect equilibrium; Static games (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:109:y:2023:i:c:s0304406823001015 DOI: 10.1016/j.jmateco.2023.102908 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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