Equilibrium with mutual organizations in adverse selection economies

We develop an equilibrium concept in the Debreu (Proc Natl Acad Sci USA 40(7):588–592, 1954) theory of value tradition for a class of adverse selection economies which includes the Spence (Q J Econ 87(3):355–374, 1973) signaling and Rothschild–Stiglitz (Q J Econ 90(4):629–649, 1976) insurance environments. The equilibrium exists and is optimal. Further, all equilibria have the same individual type utility vector. The economies are large with a finite number of types that maximize expected utility on an underlying commodity space. An implication of the analysis is that the invisible hand works for this class of adverse selection economies.