Existence of a statistical equilibrium for an economy with endogenous offer sets

A statistical equilibrium consists of distributions over offer sets of agents that can be achieved in the greatest number of ways. Although it is known that a unique equilibrium exists when the offer sets are finite and exogenous, the general case has been an open question. This paper (1) generalizes the concept of statistical equilibrium to the case where offer sets are endogenous and not necessarily finite, (2) proves the existence of equilibrium, (3) discusses a computational algorithm to obtain the equilibrium, and (4) applies the theory to the labor market and analyzes the implication of the minimum wage policy.