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 Γ-convergence of a sequence of mean-regularized instances of the original problem. The corresponding minimum points converge toward 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 Γ-convergence in economics.

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

Maggistro, Rosario
;
Pellizzari, Paolo;Tolotti, Marco
2022

Abstract

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 Γ-convergence of a sequence of mean-regularized instances of the original problem. The corresponding minimum points converge toward 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 Γ-convergence in economics.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3763530
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