# Abstract

In this note, we extend Aumann’s agreement theorem to a framework where beliefs are modelled by conditional probability systems à la Battigalli, P., and M. Siniscalchi. 1999. “Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games.” *Journal of Economic Theory* 88: 188–230. We prove two independent generalizations of the agreement theorem, one where the agents share some common conditioning event, and one where they may not.

## A Proofs

## Proof of Proposition 1.

First of all observe that

Verifying that

with eq. (10) following from

## Proof of Theorem 1.

Define

The second equality follows from

Finally, since

## Proof of Theorem 2.

*Step 1*. Define

with eq. (11) following from the fact that

*Step 2*. Now, similarly to the proof of Theorem 1, it is the case that

*Step 3*. Now take an arbitrary

with eq. (13) following again from the fact that

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## Note

I am indebted to three anonymous referees and the associate editor for their valuable comments. This note supersedes two previous papers by the same author, titled “Strong belief and agreeing to disagree” and “Hierarchies of conditional beliefs derived from commonly known priors” respectively.

**Published Online:**2018-05-04

© 2018 Walter de Gruyter GmbH, Berlin/Boston