Lexicographic agreeing to disagree and perfect equilibrium

Christian W. Bach and Jérémie Cabessa
Additional contact information
Jérémie Cabessa: DAVID - Données et algorithmes pour une ville intelligente et durable - DAVID - UVSQ - Université de Versailles Saint-Quentin-en-Yvelines

Post-Print from HAL

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; Epistemic game theory; Lexicographic probability systems; Mutual absolute continuity; Perfect equilibrium; Static games (search for similar items in EconPapers)
Date: 2023
New Economics Papers: this item is included in nep-gth and nep-mic
Note: View the original document on HAL open archive server: https://hal.science/hal-04271274v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Journal of Mathematical Economics, 2023, 109, ⟨10.1016/j.jmateco.2023.102908⟩

Downloads: (external link)
https://hal.science/hal-04271274v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04271274

DOI: 10.1016/j.jmateco.2023.102908

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().