Multiscale control of Stackelberg games

Michael Herty, Sonja Steffensen and Anna Thünen

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 200, issue C, 468-488

Abstract: We introduce a bilevel problem of the optimal control of an interacting agent system that can be interpreted as Stackelberg game with a large number of followers. It is shown that the model is well posed by providing conditions that allow to formally reduce the problem to a single level unconstrained problem. The mean-field limit is derived formally for infinitely many followers at three different stages of the optimization and the commutativity of these operations (the mean-field limit and first-order optimality on leader and on follower level) is studied. Further, we establish conditions for consistency for the relation between bilevel optimization and mean-field limit. Finally, we propose a numerical method based on the derived models and present numerical examples.

Keywords: Multi-level game; Multiscale control; Stackelberg game; Nash equilibrium; Mean-field game (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:200:y:2022:i:c:p:468-488

DOI: 10.1016/j.matcom.2022.04.028

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