The competitive equilibrium correspondence, which associates equilibrium prices of commodities and assets with allocations of endowments, identifies the preferences and beliefs of individals also under uncertainty; this is the case even if the asset market is incomplete.

Consider a group consisting of S members facing a common budget constraint p'xi=1: any demand vector belonging to the budget set can be (privately or publicly) consumed by the members. Although the intragroup decision process is not known, it is assumed to generate Pareto-efficient outcomes;...