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Multiscale Control of Stackelberg Games

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  • Michael Herty
  • Sonja Steffensen
  • Anna Thunen

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.

Suggested Citation

  • Michael Herty & Sonja Steffensen & Anna Thunen, 2020. "Multiscale Control of Stackelberg Games," Papers 2011.03405, arXiv.org.
    • Handle: RePEc:arx:papers:2011.03405
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    1. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    2. Koh, Andrew & Shepherd, Simon, 2010. "Tolling, collusion and equilibrium problems with equilibrium constraints," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 44, pages 3-22.
    3. Bensoussan, A. & Frehse, J. & Yam, S.C.P., 2017. "On the interpretation of the Master Equation," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2093-2137.
    4. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.
    5. Heinrich von Stackelberg, 2011. "Market Structure and Equilibrium," Springer Books, Springer, number 978-3-642-12586-7, January.
    6. Harks, Tobias & Schröder, Marc & Vermeulen, Dries, 2019. "Toll caps in privatized road networks," European Journal of Operational Research, Elsevier, vol. 276(3), pages 947-956.
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