Stackelberg Population Dynamics: A Predictive-Sensitivity Approach

Eduardo Mojica-Nava and Fredy Ruiz
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Eduardo Mojica-Nava: Department of Electrical and Electronics Engineering, Universidad Nacional de Colombia, Bogota 111321, Colombia
Fredy Ruiz: Dipartimento di Elettronica, Informazione e Bioingegneria—DEIB, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Games, 2021, vol. 12, issue 4, 1-15

Abstract: Hierarchical decision-making processes traditionally modeled as bilevel optimization problems are widespread in modern engineering and social systems. In this work, we deal with a leader with a population of followers in a hierarchical order of play. In general, this problem can be modeled as a leader–follower Stackelberg equilibrium problem using a mathematical program with equilibrium constraints. We propose two interconnected dynamical systems to dynamically solve a bilevel optimization problem between a leader and follower population in a single time scale by a predictive-sensitivity conditioning interconnection. For the leader’s optimization problem, we developed a gradient descent algorithm based on the total derivative, and for the followers’ optimization problem, we used the population dynamics framework to model a population of interacting strategic agents. We extended the concept of the Stackelberg population equilibrium to the differential Stackelberg population equilibrium for population dynamics. Theoretical guarantees for the stability of the proposed Stackelberg population learning dynamics are presented. Finally, a distributed energy resource coordination problem is solved via pricing dynamics based on the proposed approach. Some simulation experiments are presented to illustrate the effectiveness of the framework.

Keywords: bilevel optimization; Stackelberg games; population dynamics (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2021
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