Bach, Christian W 
ORCID: 0000-0003-0187-1820 and Cabessa, Jérémie
(2023)
Lexicographic agreeing to disagree and perfect equilibrium.
Journal of Mathematical Economics, 109.
p. 102908.
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Agreeing_and_LPS_v25.pdf - Author Accepted Manuscript Available under License Creative Commons Attribution. Download (494kB) | Preview |
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.
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Humanities and Social Sciences > School of Management |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 26 Sep 2023 07:04 |
| Last Modified: | 11 Dec 2023 15:09 |
| DOI: | 10.1016/j.jmateco.2023.102908 |
| Open Access URL: | https://doi.org/10.1016/j.jmateco.2023.102908 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3173034 |
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