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FIRST INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Ghent, Belgium

30 June - 2 July 1999

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** ELECTRONIC PROCEEDINGS **

## Antoine Billot, Alain Chateauneuf, Itzhak Gilboa, and Jean-Marc Tallon

# Sharing Beliefs: Between Agreeing and Disagreeing

** Abstract **

In an exchange economy with no aggregate uncertainty, and Bayesian agents, Pareto optimal allocations provide full insurance if and only if the agents have a common prior. It is hard to explain why there is relatively so little betting taking place. One is led to ask, when are full insurance allocations optimal for uncertainty averse agents? It turns out that commonality of beliefs, appropriately defined, is key again. Specifically, consider agents who are uncertainty averse and who maximize the minimal expected utility according to a set of possible priors. Pareto optimal allocations provide full insurance if and only if the agents share at least one prior. In the proof of this result, we develop a separation theorem among $n$ convex sets, that might be of independent interest.

** Keywords. ** Betting, multiple prior, full insurance, Pareto optimality, separation theorem.

The paper is available in the following formats:

** Authors addresses: ** Antoine Billot

CERAS_ENPC and Universite Paris II, 92, rue d'Assas, 75006 Paris, France

Alain Chateauneuf

CERMSEM, Unviversite Paris I, 106-112, bld de l'Hopital, 75647 Paris Cedex 13, France

Itzhak Gilboa

Eitan Berglas School of Economics, Tel-Aviv university, Tel-Aviv 69978, Israel

Jean-Marc Tallon

CNRS-EUREQua, 106-112, bld de l'Hopital, 75647 Paris Cedex 13, France

** E-mail addresses: **

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