IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v179y2018i1d10.1007_s10957-018-1365-7.html
   My bibliography  Save this article

Steering the Distribution of Agents in Mean-Field Games System

Author

Listed:
  • Yongxin Chen

    (Iowa State University)

  • Tryphon T. Georgiou

    (University of California)

  • Michele Pavon

    (Università di Padova)

Abstract

The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. This is formulated as a mean-field game problem, and is discussed in both non-cooperative games and cooperative games settings. In the non-cooperative games setting, a terminal cost is used to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. In the cooperative games setting, the goal is to find a common optimal control that would drive the distribution of the agents to a targeted one. We focus on the cases when the underlying dynamics is linear and the running cost is quadratic. Our approach relies on and extends the theory of optimal mass transport and its generalizations.

Suggested Citation

  • Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2018. "Steering the Distribution of Agents in Mean-Field Games System," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 332-357, October.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1365-7
    DOI: 10.1007/s10957-018-1365-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1365-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-018-1365-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    2. Alessio Porretta, 2014. "On the Planning Problem for the Mean Field Games System," Dynamic Games and Applications, Springer, vol. 4(2), pages 231-256, June.
    3. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    4. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2016. "On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 671-691, May.
    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. Jian Yang, 2021. "Analysis of Markovian Competitive Situations Using Nonatomic Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 184-216, March.
    2. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.
    3. Flavio Toxvaerd & Chryssi Giannitsarou, 2004. "Recursive global games," Money Macro and Finance (MMF) Research Group Conference 2003 104, Money Macro and Finance Research Group.
    4. Li-Hsien Sun, 2018. "Systemic Risk and Interbank Lending," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 400-424, November.
    5. Giorgio Fabbri & Salvatore Federico & Davide Fiaschi & Fausto Gozzi, 2024. "Mobility decisions, economic dynamics and epidemic," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 495-531, February.
    6. Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    7. Konishi, Hideo & Sandfort, Michael T., 2002. "Existence of stationary equilibrium in the markets for new and used durable goods," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 1029-1052, June.
    8. Ezzat Elokda & Saverio Bolognani & Andrea Censi & Florian Dorfler & Emilio Frazzoli, 2021. "Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games," Papers 2104.14662, arXiv.org, revised Jun 2024.
    9. Oberfield, Ezra & Trachter, Nicholas, 2012. "Commodity money with frequent search," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2332-2356.
    10. Ludovic Tangpi & Shichun Wang, 2022. "Optimal Bubble Riding: A Mean Field Game with Varying Entry Times," Papers 2209.04001, arXiv.org, revised Jan 2024.
    11. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    12. Boyan Jovanovic, 2004. "The Pre-Producers," NBER Working Papers 10771, National Bureau of Economic Research, Inc.
    13. Hernandez Senosiain, Patricio, 2022. "Why Do Men Keep Swiping Right? Two-Sided Search in Swipe-Based Dating Platforms," Warwick-Monash Economics Student Papers 37, Warwick Monash Economics Student Papers.
    14. James Bergin, 1999. "On the continuity of correspondences on sets of measures with restricted marginals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 471-481.
    15. Darren Filson & April Franco, 2000. "Knowledge diffusion through employee mobility," Staff Report 272, Federal Reserve Bank of Minneapolis.
    16. Xiaoli Wei & Xiang Yu & Fengyi Yuan, 2024. "Unified continuous-time q-learning for mean-field game and mean-field control problems," Papers 2407.04521, arXiv.org, revised Mar 2025.
    17. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
    18. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Papers 2105.07213, arXiv.org.
    19. Adam Copeland, 2007. "Learning Dynamics with Private and Public Signals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 523-538, June.
    20. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.

    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:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1365-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.