IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v4y2014i2p155-176.html

Mean-Field Games and Dynamic Demand Management in Power Grids

Author

Listed:
  • Fabio Bagagiolo

  • Dario Bauso

Abstract

This paper applies mean-field game theory to dynamic demand management. For a large population of electrical heating or cooling appliances (called agents), we provide a mean-field game that guarantees desynchronization of the agents thus improving the power network resilience. Second, for the game at hand, we exhibit a mean-field equilibrium, where each agent adopts a bang-bang switching control with threshold placed at a nominal temperature. At equilibrium, through an opportune design of the terminal penalty, the switching control regulates the mean temperature (computed over the population) and the mains frequency around the nominal value. To overcome Zeno phenomena we also adjust the bang-bang control by introducing a thermostat. Third, we show that the equilibrium is stable in the sense that all agents’ states, initially at different values, converge to the equilibrium value or remain confined within a given interval for an opportune initial distribution. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:4:y:2014:i:2:p:155-176
    DOI: 10.1007/s13235-013-0097-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-013-0097-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s13235-013-0097-4?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Hamidou Tembine & Quanyan Zhu & Tamer Basar, 2011. "Risk-sensitive mean field stochastic differential games," Post-Print hal-00643547, HAL.
    2. repec:dau:papers:123456789/3001 is not listed on IDEAS
    3. Oecd, 2011. "Country notes," OECD Journal on Budgeting, OECD Publishing, vol. 11(2), pages 69-213.
    4. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    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. 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, December.
    2. 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.
    3. 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.
    4. 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.
    5. Wouter Baar & Dario Bauso, 2022. "Mean Field Games on Prosumers," SN Operations Research Forum, Springer, vol. 3(4), pages 1-27, December.
    6. 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.
    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.
    8. 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.

    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. Dario Bauso & Hamidou Tembine & Tamer Başar, 2016. "Robust Mean Field Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 277-303, September.
    2. Minyi Huang, 2013. "A Mean Field Capital Accumulation Game with HARA Utility," Dynamic Games and Applications, Springer, vol. 3(4), pages 446-472, December.
    3. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    4. Flavio Toxvaerd & Chryssi Giannitsarou, 2004. "Recursive global games," Money Macro and Finance (MMF) Research Group Conference 2003 104, Money Macro and Finance Research Group.
    5. Vega-Redondo, Fernando, 1997. "Shaping long-run expectations in problems of coordination," European Journal of Political Economy, Elsevier, vol. 13(4), pages 783-806, December.
    6. A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    7. Said Hamadène & Rui Mu, 2021. "Risk-Sensitive Nonzero-Sum Stochastic Differential Game with Unbounded Coefficients," Dynamic Games and Applications, Springer, vol. 11(1), pages 84-108, March.
    8. Aïd, René & Basei, Matteo & Ferrari, Giorgio, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Center for Mathematical Economics Working Papers 679, Center for Mathematical Economics, Bielefeld University.
    9. Dianetti, Jodi & Ferrari, Giorgio & Tzouanas, Ioannis, 2023. "Ergodic Mean-Field Games of Singular Control with Regime-Switching (extended version)," Center for Mathematical Economics Working Papers 681, Center for Mathematical Economics, Bielefeld University.
    10. 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.
    11. 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.
    12. Hideo Konishi & Dimitar Simeonov, 2025. "Competing Teams in Large Markets: Free Entry Equilibrium with (Sub-)Optimal Contracts," Boston College Working Papers in Economics 1095, Boston College Department of Economics.
    13. Chakrabarti, Subir K., 2003. "Pure strategy Markov equilibrium in stochastic games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 693-724, September.
    14. Bergin, James, 2011. "Patent Length, Investment and Social Welfare," Queen's Economics Department Working Papers 274080, Queen's University - Department of Economics.
    15. Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    16. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2023. "Stationary Discounted and Ergodic Mean Field Games with Singular Controls," Mathematics of Operations Research, INFORMS, vol. 48(4), pages 1871-1898, November.
    17. 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.
    18. 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.
    19. Naci Saldi & Tamer Başar & Maxim Raginsky, 2019. "Approximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field Interactions," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1006-1033, August.
    20. Daisy J. Huang & Charles Ka Yui Leung & Chung-Yi Tse, 2018. "What Accounts for the Differences in Rent-Price Ratio and Turnover Rate? A Search-and-Matching Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 57(3), pages 431-475, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:spr:dyngam:v:4:y:2014:i:2:p:155-176. 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.