Efficient allocations and equilibria with short-selling and incomplete preferences

Abstract

This article reconsiders the theory of existence of e cient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. It is motivated by an example in the theory of assets with short-selling where there is risk and ambiguity. Agents have Bewley's incomplete preferences. As an inertia principle is assumed in markets, equilibria are individually rational. It is shown that a necessary and su cient condition for the existence of an individually rational e cient allocation or of an equilibrium is that the relative interiors of the risk adjusted sets of probabilities intersect. The more risk averse, the more ambiguity averse the agents, the more likely is an equilibrium to exist. The paper then turns to incomplete preferences represented by a family of concave utility functions. Several definitions of e ciency and of equilibrium with inertia are considered. Su cient conditions and necessary and su cient conditions are given for the existence of e cient allocations and equilibria with inertia.

Sharing ambiguous risks

“…Dana and LeVan (2014) have also shown that with maxmin expected utility preferences and incomplete Bewley preferences e¢ cient equilibrium can exist with common priors.…”