IDEAS home Printed from https://ideas.repec.org/a/aea/aecrev/v94y2004i5p1505-1535.html
   My bibliography  Save this article

When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting

Author

Listed:
  • Yan Chen
  • Robert Gazzale

Abstract

This study clarifies the conditions under which learning in games produces convergence to Nash equilibria in practice. We experimentally investigate the role of supermodularity, which is closely related to the more familiar concept of strategic complementarities, in achieving convergence through learning. Using a game from the literature on solutions to externalities, we find that supermodular and "near-supermodular" games converge significantly better than those far below the threshold of supermodularity. From a little below the threshold to the threshold, the improvement is statistically insignificant. Increasing the parameter far beyond the threshold does not significantly improve convergence.

Suggested Citation

  • Yan Chen & Robert Gazzale, 2004. "When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting," American Economic Review, American Economic Association, vol. 94(5), pages 1505-1535, December.
  • Handle: RePEc:aea:aecrev:v:94:y:2004:i:5:p:1505-1535
    Note: DOI: 10.1257/0002828043052349
    as

    Download full text from publisher

    File URL: http://www.aeaweb.org/articles.php?doi=10.1257/0002828043052349
    Download Restriction: no

    File URL: http://www.aeaweb.org/aer/data/dec04_data_gazzale.zip
    Download Restriction: no

    File URL: http://www.aeaweb.org/aer/contents/appendices/dec04_app_gazzale.zip
    Download Restriction: Access to full text is restricted to AEA members and institutional subscribers.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    2. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    3. Dybvig, Philip H. & Spatt, Chester S., 1983. "Adoption externalities as public goods," Journal of Public Economics, Elsevier, vol. 20(2), pages 231-247, March.
    4. Ho, Teck-Hua & Camerer, Colin F. & Chong, Juin-Kuan, 2001. "Economic Value of EWA Lite: A Functional Theory of Learning in Games," Working Papers 1122, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. Yasuyo Hamaguchi & Satoshi Mitani & Tatsuyoshi Saijo, 2003. "Does the Varian Mechanism Work?--Emissions Trading as an Example," International Journal of Business and Economics, College of Business and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 2(2), pages 85-96, August.
    6. Chen, Yan & Khoroshilov, Yuri, 2003. "Learning under limited information," Games and Economic Behavior, Elsevier, vol. 44(1), pages 1-25, July.
    7. Jasmina Arifovic & John Ledyard, 2002. "Computer Testbeds and Mechanism Design," Computing in Economics and Finance 2002 262, Society for Computational Economics.
    8. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.
    9. Boylan Richard T. & El-Gamal Mahmoud A., 1993. "Fictitious Play: A Statistical Study of Multiple Economic Experiments," Games and Economic Behavior, Elsevier, vol. 5(2), pages 205-222, April.
    10. Josef Falkinger, 2000. "A Simple Mechanism for the Efficient Provision of Public Goods: Experimental Evidence," American Economic Review, American Economic Association, vol. 90(1), pages 247-264, March.
    11. Andreoni,J. & Varian,H., 1999. "Pre-play contracting in the prisoners' dilemma," Working papers 18, Wisconsin Madison - Social Systems.
    12. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    13. Harstad, Ronald M. & Marrese, Michael, 1982. "Behavioral explanations of efficient public good allocations," Journal of Public Economics, Elsevier, vol. 19(3), pages 367-383, December.
    14. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    15. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    16. Chen, Yan, 2008. "Incentive-compatible Mechanisms for Pure Public Goods: A Survey of Experimental Research," Handbook of Experimental Economics Results, Elsevier.
    17. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    18. Yan Chen & Fang-Fang Tang, 1998. "Learning and Incentive-Compatible Mechanisms for Public Goods Provision: An Experimental Study," Journal of Political Economy, University of Chicago Press, vol. 106(3), pages 633-662, June.
    19. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, Oxford University Press, vol. 103(3), pages 441-463.
    20. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    21. Postlewaite, Andrew & Vives, Xavier, 1987. "Bank Runs as an Equilibrium Phenomenon," Journal of Political Economy, University of Chicago Press, vol. 95(3), pages 485-491, June.
    22. Smith, Vernon L, 1979. " An Experimental Comparison of Three Public Good Decision Mechanisms," Scandinavian Journal of Economics, Wiley Blackwell, vol. 81(2), pages 198-215.
    23. Cox, James C. & Walker, Mark, 1998. "Learning to play Cournot duopoly strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 36(2), pages 141-161, August.
    24. Varian, Hal R, 1994. "A Solution to the Problem of Externalities When Agents Are Well-Informed," American Economic Review, American Economic Association, vol. 84(5), pages 1278-1293, December.
    25. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    26. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
    27. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
    28. Falkinger, Josef, 1996. "Efficient private provision of public goods by rewarding deviations from average," Journal of Public Economics, Elsevier, vol. 62(3), pages 413-422, November.
    29. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - 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:aea:aecrev:v:94:y:2004:i:5:p:1505-1535. 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: (Jane Voros) or (Michael P. Albert). General contact details of provider: http://edirc.repec.org/data/aeaaaea.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.