IDEAS home Printed from https://ideas.repec.org/p/hhs/bergec/2002_009.html
   My bibliography  Save this paper

Stochastic Approximation, Momentum, and Nash Play

Author

Listed:

Abstract

Main objects here are normal-form games, featuring uncertainty and noncooperative players who entertain local visions, form local approximations, and hesitate in making large, swift adjustments. For the purpose of reaching Nash equilibrium, or learning such play, we advocate and illustrate an algorithm that combines stochastic gradient projection with the heavyball method. What emerges is a coupled, constrained, second-order stochastic process. Some friction feeds into and stabilizes myopic approximations. Convergence to Nash play obtains under seemingly weak and natural conditions, an important one being that accumulated marginal payoffs remains bounded above.

Suggested Citation

  • Berglann, Helge & Flåm, Sjur Didrik, 2002. "Stochastic Approximation, Momentum, and Nash Play," Working Papers in Economics 09/02, University of Bergen, Department of Economics.
    • Handle: RePEc:hhs:bergec:2002_009
    as

    Download full text from publisher

    File URL: http://ekstern.filer.uib.no/svf/2002/09-02_1.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    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. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    3. S. D. Flåm & J. Morgan, 2004. "Newtonian Mechanics And Nash Play," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 181-194.
    4. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    5. Flam, Sjur Didrik, 1996. "Approaches to economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1505-1522.
    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. Sjur Didrik Flåm, 2002. "Convexity, Differential Equations, and Games," CESifo Working Paper Series 655, CESifo.
    2. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    3. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    4. Subhasish Dugar & Arnab Mitra, 2016. "Bertrand Competition With Asymmetric Marginal Costs," Economic Inquiry, Western Economic Association International, vol. 54(3), pages 1631-1647, July.
    5. van Damme, E.E.C., 2000. "Non-cooperative Games," Other publications TiSEM 51465233-a356-4d20-acc4-c, Tilburg University, School of Economics and Management.
    6. Erlei, Mathias, 2008. "Heterogeneous social preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 436-457, March.
    7. van Damme, E.E.C., 2015. "Game theory : Noncooperative games," Other publications TiSEM ff518f2b-501f-4d99-817b-c, Tilburg University, School of Economics and Management.
    8. He, Simin & Wu, Jiabin, 2020. "Compromise and coordination: An experimental study," Games and Economic Behavior, Elsevier, vol. 119(C), pages 216-233.
    9. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    10. Tilman Slembeck, 2000. "Learning in Economics: Where Do We Stand?," Microeconomics 0004007, University Library of Munich, Germany.
    11. Heggedal, Tom-Reiel & Helland, Leif, 2014. "Platform selection in the lab," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 168-177.
    12. Giovanna Devetag, 2000. "Coordination in "Critical Mass" Games: An Experimental Study," LEM Papers Series 2000/03, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    13. Dolan, Paul & Galizzi, Matteo M., 2015. "Like ripples on a pond: Behavioral spillovers and their implications for research and policy," Journal of Economic Psychology, Elsevier, vol. 47(C), pages 1-16.
    14. Rutstrom, E. Elizabet & Wilcox, Nathaniel, 2008. "Stated versus inferred beliefs: A methodological inquiry and experimental test," MPRA Paper 11852, University Library of Munich, Germany.
    15. Heiko Rauhut, 2015. "Stronger inspection incentives, less crime? Further experimental evidence on inspection games," Rationality and Society, , vol. 27(4), pages 414-454, November.
    16. Rutström, E. Elisabet & Wilcox, Nathaniel T., 2009. "Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test," Games and Economic Behavior, Elsevier, vol. 67(2), pages 616-632, November.
    17. Nathaniel T Wilcox, 2003. "Heterogeneity and Learning Principles," Levine's Bibliography 666156000000000435, UCLA Department of Economics.
    18. Giovanna Devetag, 2003. "Coordination and Information in Critical Mass Games: An Experimental Study," Experimental Economics, Springer;Economic Science Association, vol. 6(1), pages 53-73, June.
    19. Teck-Hua Ho & So-Eun Park & Xuanming Su, 2021. "A Bayesian Level- k Model in n -Person Games," Management Science, INFORMS, vol. 67(3), pages 1622-1638, March.
    20. 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.

    More about this item

    Keywords

    Noncooperative games; Nash equilibrium; stochastic programming and approximation; the heavy ball method.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    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:hhs:bergec:2002_009. 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: Kjell Erik Lommerud (email available below). General contact details of provider: https://edirc.repec.org/data/iouibno.html .

    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.