Weak equilibria of a mean-field market model under asymmetric information

Abstract

We investigate how asymmetric information affects equilibrium price formation in an economy with many interacting agents. Motivated by a finite-player model with two populations of asymmetrically informed agents, we study its mean-field limit when one population observes an additional stochastic factor which is inaccessible to the other. The resulting equilibrium condition involves the conditional expectation of the adjoint process and, therefore, differs from standard mean-field formulations based on the state process. We prove existence of mean-field equilibria in probabilistic weak sense by combining discretization and weak convergence arguments with a lifting procedure tailored to preserve compatibility in the limit. Under additional assumptions, we obtain a conditional asymptotic justification of the mean-field price as an approximation of the finite-player market clearing relation. Finally, we illustrate how, in the case of a single informed agent, her strategy can be characterized in terms of the equilibrium.