Advanced Search
MyIDEAS: Login to save this article or follow this journal

Dynamics in near-potential games

Contents:

Author Info

  • Candogan, Ozan
  • Ozdaglar, Asuman
  • Parrilo, Pablo A.
Registered author(s):

    Abstract

    We consider discrete-time learning dynamics in finite strategic form games, and show that games that are close to a potential game inherit many of the dynamical properties of potential games. We first study the evolution of the sequence of pure strategy profiles under better/best response dynamics. We show that this sequence converges to a (pure) approximate equilibrium set whose size is a function of the “distance” to a given nearby potential game. We then focus on logit response dynamics, and provide a characterization of the limiting outcome in terms of the distance of the game to a given potential game and the corresponding potential function. Finally, we turn attention to fictitious play, and establish that in near-potential games the sequence of empirical frequencies of player actions converges to a neighborhood of (mixed) equilibria, where the size of the neighborhood increases according to the distance to the set of potential games.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613000948
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 82 (2013)
    Issue (Month): C ()
    Pages: 66-90

    as in new window
    Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:66-90

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Dynamics in games; Near-potential games; Best response dynamics; Logit response dynamics; Fictitious play;

    Find related papers by JEL classification:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Anantharam, V. & Tsoucas, P., 1989. "A proof of the Markov chain tree theorem," Statistics & Probability Letters, Elsevier, Elsevier, vol. 8(2), pages 189-192, June.
    2. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, Elsevier, vol. 5(3), pages 387-424, July.
    3. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
    4. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Levine's Bibliography 666156000000000420, UCLA Department of Economics.
    5. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, Elsevier, vol. 68(1), pages 258-265, January.
    6. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2265-2294, November.
    7. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Economics Working Papers, Institute for Advanced Study, School of Social Science 0085, Institute for Advanced Study, School of Social Science.
    8. smorris & Takashi Ui, 2004. "Generalized Potentials and Robust Sets of Equilibria," Econometric Society 2004 North American Winter Meetings 45, Econometric Society.
    9. 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.
    10. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
    11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
    12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 124-143, May.
    13. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, Elsevier, vol. 68(2), pages 413-427, March.
    14. Morris, Stephen Morris & Takashi Ui, 2002. "Best Response Equivalence," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1377, Cowles Foundation for Research in Economics, Yale University.
    15. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, Elsevier, vol. 54(1), pages 77-94, January.
    16. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
    17. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 5(3), pages 368-386, July.
    18. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    19. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199269181, October.
    20. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
    21. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1255-77, November.
    22. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:66-90. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.