Approximate solutions for crowd-averse robust mean-field games

Abstract

We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowd-averse”. For this game we first illustrate the paradigm of robust mean-field games. Second, we provide a new approximate solution approach based on the extension of the state space and prove the existence of equilibria and their stability properties.