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

Abstract: We investigate how asymmetric information affects the equilibrium dynamics in a setting where a large number of players interacts. Motivated by the analysis of the mechanism of equilibrium price formation, we consider the mean-field limit of a model with two subpopulations of asymmetrically informed players. One subpopulation observes a stochastic factor that remains inaccessible to the other. We derive an equation for the mean-field equilibrium and prove the existence of solutions in probabilistic weak sense. We rely on a discretization of the trajectories and on weak convergence arguments. We also study the conditions under which a mean-field equilibrium provides an approximation of the equilibrium price for an economy populated by finitely many players. Finally, we illustrate how, in the case of a single informed agent, her strategy can be characterized in terms of the equilibrium.