Multiscale Control of Stackelberg Games
Michael Herty, Sonja Steffensen, Anna Th\"unen
TL;DR
This paper studies a large-scale linear-quadratic Stackelberg game with many followers, explores its mean-field limit, and develops a numerical method for solving the models, providing insights into the relationship between optimization and mean-field behavior.
Contribution
It introduces a mean-field framework for Stackelberg games with numerous followers and proposes a numerical approach based on the derived models.
Findings
Established conditions for consistency between optimization and mean-field limit.
Derived the mean-field limit for infinitely many followers.
Developed a numerical method and demonstrated its effectiveness.
Abstract
We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for consistency are established. Finally, we propose a numerical method based on the derived models and present numerical results.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Partial Differential Equations · Nonlinear Differential Equations Analysis