Dangerous Tangents: An Application of Γ-Convergence to the Control of Dynamical Systems

34 Pages Posted: 28 Apr 2021 Last revised: 16 May 2022

See all articles by Rosario Maggistro

Rosario Maggistro

University of Trieste

Paolo Pellizzari

Ca Foscari University of Venice - Dipartimento di Economia

Elena Sartori

University of Padua - Department of Mathematics "Tullio Levi-Civita"

Marco Tolotti

Ca Foscari University of Venice - Department of Management

Date Written: May 16, 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 $\Gamma$-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

Maggistro, Rosario and Pellizzari, Paolo and Sartori, Elena and Tolotti, Marco, Dangerous Tangents: An Application of Γ-Convergence to the Control of Dynamical Systems (May 16, 2022). Available at SSRN: https://ssrn.com/abstract=3835319 or http://dx.doi.org/10.2139/ssrn.3835319

Rosario Maggistro (Contact Author)

University of Trieste ( email )

Piazzale Europa, 1
Trieste, Trieste 34100
Italy

Paolo Pellizzari

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

Elena Sartori

University of Padua - Department of Mathematics "Tullio Levi-Civita" ( email )

Italy

Marco Tolotti

Ca Foscari University of Venice - Department of Management ( email )

San Giobbe, Cannaregio 873
Venice, 30121
Italy

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