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

Rosario Maggistro (), Paolo Pellizzari, Elena Sartori () and Marco Tolotti
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Rosario Maggistro: University of Trieste
Elena Sartori: University of Padova

Decisions in Economics and Finance, 2022, vol. 45, issue 2, No 1, 480 pages

Abstract: 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 $$\Gamma $$ 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 $$\Gamma $$ Γ -convergence in economics.

Keywords: Dynamical systems; Finite population dynamics; $$\Gamma $$ Γ -convergence; Saddle-node bifurcations; Social interaction; 91B14; 49J45; C61; C63; D91 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10203-022-00372-z

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