IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v53y2024i1d10.1007_s00182-023-00866-z.html
   My bibliography  Save this article

A myopic adjustment process for mean field games with finite state and action space

Author

Listed:
  • Berenice Anne Neumann

    (Trier University)

Abstract

In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations is the complexity of the computations necessary to determine dynamic mean field equilibria, which makes it seem questionable whether agents are indeed able to play these equilibria. We prove that the myopic adjustment process converges locally towards strict stationary equilibria under rather broad conditions. Moreover, we also obtain a global convergence result under stronger, yet intuitive conditions.

Suggested Citation

  • Berenice Anne Neumann, 2024. "A myopic adjustment process for mean field games with finite state and action space," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(1), pages 159-195, March.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:1:d:10.1007_s00182-023-00866-z
    DOI: 10.1007/s00182-023-00866-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-023-00866-z
    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/s00182-023-00866-z?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. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. V. N. Kolokoltsov & O. A. Malafeyev, 2018. "Corruption and botnet defense: a mean field game approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 977-999, September.
    3. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    4. Damien Besancenot & Habib Dogguy, 2015. "Paradigm Shift: A Mean Field Game Approach," Bulletin of Economic Research, Wiley Blackwell, vol. 67(3), pages 289-302, July.
    5. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    6. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. V. N. Kolokoltsov & O. A. Malafeyev, 2017. "Mean-Field-Game Model of Corruption," Dynamic Games and Applications, Springer, vol. 7(1), pages 34-47, March.
    8. Berenice Anne Neumann, 2020. "Stationary Equilibria of Mean Field Games with Finite State and Action Space," Dynamic Games and Applications, Springer, vol. 10(4), pages 845-871, December.
    9. René Carmona & Peiqi Wang, 2021. "A Probabilistic Approach to Extended Finite State Mean Field Games," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 471-502, 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. Neumann, Berenice Anne, 2022. "Essential stationary equilibria of mean field games with finite state and action space," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 85-91.
    2. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    3. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    4. Berenice Anne Neumann, 2020. "A Myopic Adjustment Process for Mean Field Games with Finite State and Action Space," Papers 2008.13420, arXiv.org.
    5. Dai Zusai, 2023. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1215-1260, December.
    6. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2022. "Generalized perturbed best response dynamics with a continuum of strategies," Journal of Economic Theory, Elsevier, vol. 200(C).
    7. William Sandholm, 2014. "Probabilistic Interpretations of Integrability for Game Dynamics," Dynamic Games and Applications, Springer, vol. 4(1), pages 95-106, March.
    8. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.
    9. Sawa, Ryoji & Zusai, Dai, 2019. "Evolutionary dynamics in multitasking environments," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 288-308.
    10. John Asker & Chaim Fershtman & Jihye Jeon & Ariel Pakes, 2020. "A computational framework for analyzing dynamic auctions: The market impact of information sharing," RAND Journal of Economics, RAND Corporation, vol. 51(3), pages 805-839, September.
    11. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    12. Lu-ping Liu & Wen-sheng Jia, 2024. "Well-Posedness for Mean Field Games with Finite State and Action Space," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 36-53, April.
    13. RatulLahkar & Sayan Mukherjee & Souvik Roy, 2021. "Generalized Perturbed Best Response Dynamics with a Continuum of Strategies," Working Papers 51, Ashoka University, Department of Economics.
    14. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    15. William H. Sandholm & Mathias Staudigl, 2018. "Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1348-1377, November.
    16. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
    17. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    18. Pietro Dindo & Jan Tuinstra, 2011. "A Class of Evolutionary Models for Participation Games with Negative Feedback," Computational Economics, Springer;Society for Computational Economics, vol. 37(3), pages 267-300, March.
    19. John Asker & Chaim Fershtman & Jihye Jeon & Ariel Pakes, 2016. "The Competitive Effects of Information Sharing," NBER Working Papers 22836, National Bureau of Economic Research, Inc.
    20. Berenice Anne Neumann, 2020. "Stationary Equilibria of Mean Field Games with Finite State and Action Space," Dynamic Games and Applications, Springer, vol. 10(4), pages 845-871, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

    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:jogath:v:53:y:2024:i:1:d:10.1007_s00182-023-00866-z. 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.