IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2011.03405.html
   My bibliography  Save this paper

Multiscale Control of Stackelberg Games

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2011.03405
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Herty, Michael & Steffensen, Sonja & Thünen, Anna, 2022. "Multiscale control of Stackelberg games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 468-488.
    2. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2021. "A Local Variation Method for Bilevel Nash Equilibrium Problems," CSEF Working Papers 620, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    3. Michael Herty & Sonja Steffensen & Anna Thunen, 2018. "Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response," Papers 1808.07941, arXiv.org, revised Apr 2020.
    4. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    5. Christos N. Dimitriadis & Evangelos G. Tsimopoulos & Michael C. Georgiadis, 2021. "A Review on the Complementarity Modelling in Competitive Electricity Markets," Energies, MDPI, vol. 14(21), pages 1-27, November.
    6. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    7. Shang, Lihui & Zhao, Mingming & Ai, Jun & Su, Zhan, 2021. "Opinion evolution in the Sznajd model on interdependent chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    8. Lu, Xi & Mo, Hongming & Deng, Yong, 2015. "An evidential opinion dynamics model based on heterogeneous social influential power," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 98-107.
    9. Andreas Koulouris & Ioannis Katerelos & Theodore Tsekeris, 2013. "Multi-Equilibria Regulation Agent-Based Model of Opinion Dynamics in Social Networks," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 11(1), pages 51-70.
    10. Grimm, Veronika & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2017. "Uniqueness of market equilibrium on a network: A peak-load pricing approach," European Journal of Operational Research, Elsevier, vol. 261(3), pages 971-983.
    11. Guo, Xin & Pham, Huyên & Wei, Xiaoli, 2023. "Itô’s formula for flows of measures on semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 350-390.
    12. Clémence Alasseur & Imen Ben Taher & Anis Matoussi, 2020. "An Extended Mean Field Game for Storage in Smart Grids," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 644-670, February.
    13. Martin Weibelzahl & Alexandra Märtz, 2020. "Optimal storage and transmission investments in a bilevel electricity market model," Annals of Operations Research, Springer, vol. 287(2), pages 911-940, April.
    14. Pär Holmberg & Andy Philpott, 2014. "Supply function equilibria in transportation networks," Cambridge Working Papers in Economics 1421, Faculty of Economics, University of Cambridge.
    15. Thomas Moore & Patrick Finley & Nancy Brodsky & Theresa Brown & Benjamin Apelberg & Bridget Ambrose & Robert Glass, 2015. "Modeling Education and Advertising with Opinion Dynamics," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 18(2), pages 1-7.
    16. George Butler & Gabriella Pigozzi & Juliette Rouchier, 2019. "Mixing Dyadic and Deliberative Opinion Dynamics in an Agent-Based Model of Group Decision-Making," Complexity, Hindawi, vol. 2019, pages 1-31, August.
    17. Huang, Changwei & Hou, Yongzhao & Han, Wenchen, 2023. "Coevolution of consensus and cooperation in evolutionary Hegselmann–Krause dilemma with the cooperation cost," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    18. María Cecilia Gimenez & Luis Reinaudi & Ana Pamela Paz-García & Paulo Marcelo Centres & Antonio José Ramirez-Pastor, 2021. "Opinion evolution in the presence of constant propaganda: homogeneous and localized cases," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-11, January.
    19. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska, 2023. "On the Design of Public Debate in Social Networks," Operations Research, INFORMS, vol. 71(2), pages 626-648, March.
    20. Kułakowski, Krzysztof, 2009. "Opinion polarization in the Receipt–Accept–Sample model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 469-476.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2011.03405. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.