Weak equilibria of a mean-field market model under asymmetric information
Alekos Cecchin, Markus Fischer, Claudio Fontana, Giacomo Lanaro
TL;DR
This work develops a mean-field framework for a market with asymmetric information across two agent types, deriving a mean-field equation for the equilibrium price and proving the existence of a weak lifted mean-field equilibrium via a discretization-and-convergence approach. The authors define a precise weak lifting of MF equilibria, prove an existence theorem, and show that, under linear-affine cost structures, an unlifted (strong) MF equilibrium also exists. They connect the MF analysis to finite-agent economies through an asymptotic market-clearing perspective and provide a detailed discretization scheme (with fixed-point arguments) and stability analysis to justify the MF approximation for large but finite populations. A special case with one informed agent demonstrates explicit structure and information revelation through the equilibrium price. Overall, the paper advances rigorous MF tools for price formation under information asymmetry, clarifying when MF equilibria approximate finite economies and how information propagates via the equilibrium price.
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.