Dangerous Tangents: An Application of Γ-Convergence to the Control of Dynamical Systems
34 Pages Posted: 28 Apr 2021 Last revised: 16 May 2022
Date Written: May 16, 2022
Inspired by the classical riot model proposed by Granovetter in 1978, we consider a parametric stochastic dynamical system that describes the collective behavior of a large population of interacting agents. By controlling a parameter, a policy maker seeks to minimize her own disutility, 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 the $\Gamma$-convergence of a sequence of mean-regularized instances of the original problem. The corresponding minimum points converge towards a unique value that 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.
Keywords: Dynamical Systems, Finite Population Dynamics, Γ-convergence, Saddle-node Bifurcations, Social Interaction
JEL Classification: C61, C63, D91
Suggested Citation: Suggested Citation