IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.13420.html
   My bibliography  Save this paper

A Myopic Adjustment Process for Mean Field Games with Finite State and Action Space

Author

Listed:
  • Berenice Anne Neumann

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 are the complex computations necessary to determine dynamic mean-field equilibria, which make it seem questionable whether agents are indeed able to play these equilibria. We prove that the myopic adjustment process converges locally towards stationary equilibria with deterministic equilibrium strategies under rather broad conditions. Moreover, for a two-strategy setting, we also obtain a global convergence result under stronger, yet intuitive conditions.

Suggested Citation

  • Berenice Anne Neumann, 2020. "A Myopic Adjustment Process for Mean Field Games with Finite State and Action Space," Papers 2008.13420, arXiv.org.
    • Handle: RePEc:arx:papers:2008.13420
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.13420
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Damien Besancenot & Habib Dogguy, 2011. "Paradigm Shift," CEPN Working Papers halshs-00590527, HAL.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. 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.
    4. 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.
    5. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    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. 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.

    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. Galbiati, Marco & Soramäki, Kimmo, 2011. "An agent-based model of payment systems," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 859-875, June.
    2. Ekmekci, Mehmet & Gossner, Olivier & Wilson, Andrea, 2012. "Impermanent types and permanent reputations," Journal of Economic Theory, Elsevier, vol. 147(1), pages 162-178.
    3. Laurent Lamy, 2013. "“Upping the ante”: how to design efficient auctions with entry?," RAND Journal of Economics, RAND Corporation, vol. 44(2), pages 194-214, June.
    4. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    5. Mathieu Faure & Gregory Roth, 2010. "Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 624-640, August.
    6. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    7. ,, 2011. "Manipulative auction design," Theoretical Economics, Econometric Society, vol. 6(2), May.
    8. 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.
    9. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    10. Saori Iwanaga & Akira Namatame, 2015. "Hub Agents Determine Collective Behavior," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 165-181.
    11. Erhao Xie, 2019. "Monetary Payoff and Utility Function in Adaptive Learning Models," Staff Working Papers 19-50, Bank of Canada.
    12. Jacob W. Crandall & Mayada Oudah & Tennom & Fatimah Ishowo-Oloko & Sherief Abdallah & Jean-François Bonnefon & Manuel Cebrian & Azim Shariff & Michael A. Goodrich & Iyad Rahwan, 2018. "Cooperating with machines," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
      • Abdallah, Sherief & Bonnefon, Jean-François & Cebrian, Manuel & Crandall, Jacob W. & Ishowo-Oloko, Fatimah & Oudah, Mayada & Rahwan, Iyad & Shariff, Azim & Tennom,, 2017. "Cooperating with Machines," TSE Working Papers 17-806, Toulouse School of Economics (TSE).
      • Abdallah, Sherief & Bonnefon, Jean-François & Cebrian, Manuel & Crandall, Jacob W. & Ishowo-Oloko, Fatimah & Oudah, Mayada & Rahwan, Iyad & Shariff, Azim & Tennom,, 2017. "Cooperating with Machines," IAST Working Papers 17-68, Institute for Advanced Study in Toulouse (IAST).
      • Jacob Crandall & Mayada Oudah & Fatimah Ishowo-Oloko Tennom & Fatimah Ishowo-Oloko & Sherief Abdallah & Jean-François Bonnefon & Manuel Cebrian & Azim Shariff & Michael Goodrich & Iyad Rahwan, 2018. "Cooperating with machines," Post-Print hal-01897802, HAL.
    13. Dieter Balkenborg & Rosemarie Nagel, 2016. "An Experiment on Forward vs. Backward Induction: How Fairness and Level k Reasoning Matter," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 378-408, August.
    14. B Kelsey Jack, 2009. "Auctioning Conservation Contracts in Indonesia - Participant Learning in Multiple Trial Rounds," CID Working Papers 35, Center for International Development at Harvard University.
    15. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    16. William L. Cooper & Tito Homem-de-Mello & Anton J. Kleywegt, 2015. "Learning and Pricing with Models That Do Not Explicitly Incorporate Competition," Operations Research, INFORMS, vol. 63(1), pages 86-103, February.
    17. Carlos Alós-Ferrer & Georg Kirchsteiger & Markus Walzl, 2010. "On the Evolution of Market Institutions: The Platform Design Paradox," Economic Journal, Royal Economic Society, vol. 120(543), pages 215-243, March.
    18. Siegfried Berninghaus & Werner Güth & M. Vittoria Levati & Jianying Qiu, 2006. "Satisficing in sales competition: experimental evidence," Papers on Strategic Interaction 2006-32, Max Planck Institute of Economics, Strategic Interaction Group.
    19. Cho, In-Koo, 2005. "Introduction to learning and bounded rationality," Journal of Economic Theory, Elsevier, vol. 124(2), pages 127-128, October.
    20. Ball, Richard, 2017. "Violations of monotonicity in evolutionary models with sample-based beliefs," Economics Letters, Elsevier, vol. 152(C), pages 100-104.

    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:2008.13420. 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.