Efficient allocations under ambiguity

An important implication of the expected utility model under risk aversion is that if agents have the same probability belief, then the efficient allocations under uncertainty are comonotone with the aggregate endowment, and if their beliefs are concordant, then the efficient allocations are measurable with respect to the aggregate endowment. We study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional belief, which we introduce in this paper. We provide characterizations of such conditional beliefs for the standard models of preferences used in applications. We are grateful to an associate editor and three anonymous referees for useful suggestions. We thank the audiences at the conference in honor of Truman Bewley at the University of Texas, Austin, at EWGET in Barcelona, 2009 SAET Conference on Ischia, SWET 09 at Universite Paris I, 2009 NSF-NBER-CEME Conference in San Diego, the 6th Annual Cowles G.E. Conference at Yale and EUI in Florence. We thank José Luis Montiel Olea for proofreading. A part of this research was done while Strzalecki was visiting the Economic Theory Center at Princeton University to which he is very grateful for its support and hospitality.