Risk sharing in the small and in the large

This paper analyzes risk sharing in economies with no aggregate uncertainty when agents have non-convex preferences. In particular, agents need not be globally risk-averse, or uncertainty-averse in the sense of Schmeidler (1989). We identify a behavioral condition under which betting is inefficient (i.e., every Pareto-efficient allocation provides full insurance, and conversely) if and only if agents’ supporting probabilities (defined as in Rigotti et al., 2008) have a non-empty intersection. Our condition is consistent with empirical and experimental evidence documenting violations of convexity in either outcomes or utilities. Our results show that the connection between speculative betting and inconsistent beliefs does not depend upon global notions of risk or ambiguity aversion.