Aumann's Agreement Theorem

Source: url:https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6837298 Authors: Ruiz Chen, Ben Eltschig, Ken Ono, Jujian Zhang Status: verified Main declarations: AgreeToDisagree.agreeToDisagree, AgreeToDisagree.agreeToDisagree_beliefs Tags: probability, game-theory, epistemic-logic MSC: 60A10, 91A40

Mathematical overview

This project formalizes Aumann's theorem that agents with common prior probabilities cannot agree to disagree when it is common knowledge that they assign fixed posterior probabilities to an event.

The first theorem proves equality of the posteriors under common knowledge for two agents and, more generally, a family of agents. The second develops a p-belief variant, proving that common p-belief bounds posterior disagreement by 2 * (1 - p).

Main results

• AgreeToDisagree.agreeToDisagree — two agents with common knowledge of their posteriors and equal common prior posterior on the common-knowledge cell have equal posteriors.
• AgreeToDisagree.agreeToDisagree' — the corresponding finite-family formulation.
• AgreeToDisagree.agreeToDisagree_beliefs — common p-belief bounds posterior disagreement by 2 * (1 - p).