IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v173y2017i2d10.1007_s10957-017-1078-3.html
   My bibliography  Save this article

Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

Author

Listed:
  • Fabio Bagagiolo

    (University of Trento)

  • Dario Bauso

    (University of Sheffield)

  • Rosario Maggistro

    (University of Trento)

  • Marta Zoppello

    (University of Trento)

Abstract

This paper studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. The stability of the system is illustrated via numerical studies.

Suggested Citation

  • Fabio Bagagiolo & Dario Bauso & Rosario Maggistro & Marta Zoppello, 2017. "Game Theoretic Decentralized Feedback Controls in Markov Jump Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 704-726, May.
  • Handle: RePEc:spr:joptap:v:173:y:2017:i:2:d:10.1007_s10957-017-1078-3
    DOI: 10.1007/s10957-017-1078-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1078-3
    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/s10957-017-1078-3?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. Fabio Bagagiolo & Dario Bauso, 2014. "Mean-Field Games and Dynamic Demand Management in Power Grids," Dynamic Games and Applications, Springer, vol. 4(2), pages 155-176, June.
    2. repec:dau:papers:123456789/3001 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fabio Bagagiolo & Silvia Faggian & Rosario Maggistro & Raffaele Pesenti, 2022. "Optimal Control of the Mean Field Equilibrium for a Pedestrian Tourists’ Flow Model," Networks and Spatial Economics, Springer, vol. 22(2), pages 243-266, June.

    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. Yunhan Huang & Quanyan Zhu, 2022. "Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review," Dynamic Games and Applications, Springer, vol. 12(1), pages 7-48, March.
    2. Antonio Paola & David Angeli & Goran Strbac, 2018. "On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market," Dynamic Games and Applications, Springer, vol. 8(4), pages 761-798, December.
    3. Fabio Bagagiolo & Dario Bauso & Raffaele Pesenti, 2016. "Mean-Field Game Modeling the Bandwagon Effect with Activation Costs," Dynamic Games and Applications, Springer, vol. 6(4), pages 456-476, December.
    4. Ellen Webborn & Robert S. MacKay, 2017. "A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control," Complexity, Hindawi, vol. 2017, pages 1-26, December.
    5. Roxana Dumitrescu & Marcos Leutscher & Peter Tankov, 2024. "Energy transition under scenario uncertainty: a mean-field game of stopping with common noise," Mathematics and Financial Economics, Springer, volume 18, number 4, October.
    6. Wouter Baar & Dario Bauso, 2022. "Mean Field Games on Prosumers," SN Operations Research Forum, Springer, vol. 3(4), pages 1-27, December.
    7. Joseph Andria & Rosario Maggistro & Raffaele Pesenti, 2023. "Sustainable Management of Tourist Flow Networks: A Mean Field Model," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 730-761, February.

    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:173:y:2017:i:2:d:10.1007_s10957-017-1078-3. 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.