Dangerous tangents: an application of Γ-convergence to the control of dynamical systems

Inspired by the classical riot model proposed by Granovetter in 1978, we consider a parametric stochastic dynamical system describing the collective behavior of a large population of interacting agents. By controlling a parameter, a policy maker aims at maximizing her own utility which, in turn, depends on the steady state of the system. We show that this economically sensible optimization is ill-posed and illustrate a novel way to tackle this practical and formal issue. Our approach is based on Gamma-convergence of a sequence of mean-regularized instances of the original problem. The corresponding maximizers converge towards a unique value which intuitively is the solution of the original ill-posed problem. Notably, to the best of our knowledge, this is one of the first applications of Gamma-convergence in economics.