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

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Author Info
Yan Chen
Robert Gazzale

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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.

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Article provided by American Economic Association in its journal American Economic Review.

Volume (Year): 94 (2004)
Issue (Month): 5 (December)
Pages: 1505-1535
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Handle: RePEc:aea:aecrev:v:94:y:2004:i:5:p:1505-1535

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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.:
  1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
  6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  7. Yasuyo Hamaguchi & Satoshi Mitani & Tatsuyoshi Saijo, 2004. "Does the Varian Mechanism Work? -Emissions Trading as an Example," Discussion papers 04009, Research Institute of Economy, Trade and Industry (RIETI). [Downloadable!]
  8. Chen, Yan & Khoroshilov, Yuri, 2003. "Learning under limited information," Games and Economic Behavior, Elsevier, vol. 44(1), pages 1-25, July. [Downloadable!] (restricted)
  9. Jasmina Arifovic & John Ledyard, 2002. "Computer Testbeds and Mechanism Design," Computing in Economics and Finance 2002 262, Society for Computational Economics. [Downloadable!]
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  11. Josef Falkinger et al., 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. [Downloadable!] (restricted)
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  12. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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  13. Postlewaite, Andrew & Vives, Xavier, 1987. "Bank Runs as an Equilibrium Phenomenon," Journal of Political Economy, University of Chicago Press, vol. 95(3), pages 485-91, June. [Downloadable!] (restricted)
  14. Smith, Vernon L, 1979. " An Experimental Comparison of Three Public Good Decision Mechanisms," Scandinavian Journal of Economics, Blackwell Publishing, vol. 81(2), pages 198-215.
  15. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August. [Downloadable!] (restricted)
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  16. 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. [Downloadable!] (restricted)
  17. Hal R. Varian, 1994. "A Solution to the Problem of Externalities when Agents are Well-Informed}," Microeconomics 9401003, EconWPA. [Downloadable!]
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  18. 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. [Downloadable!] (restricted)
  19. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February. [Downloadable!] (restricted)
  20. 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. [Downloadable!] (restricted)
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  22. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  23. 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. [Downloadable!] (restricted)
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  28. 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 234-48, March. [Downloadable!] (restricted)
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(explanations, 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.)

  1. Yasuyo Hamaguchi & Satoshi Mitani & Tatsuyoshi Saijo, 2004. "Does the Varian Mechanism Work? -Emissions Trading as an Example," Discussion papers 04009, Research Institute of Economy, Trade and Industry (RIETI). [Downloadable!]
  2. Juergen Bracht & Charles Figuières & Marisa Ratto, 2004. "Relative performance of two simple incentive mechanisms in a public good experiment," IDEP Working Papers 0409, Institut d'economie publique (IDEP), Marseille, France. [Downloadable!]
    Other versions:
  3. Van Essen, Matthew J., 2008. "A Simple Supermodular Mechanism that Implements Lindahl Allocations," MPRA Paper 12781, University Library of Munich, Germany. [Downloadable!]
  4. Potters, Jan & Suetens, Sigrid, 2006. "Cooperation in experimental games of strategic complements and substitutes," Discussion Paper 48, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  5. Timothy N. Cason & Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation Experiments: Do Strategy-proof Mechanisms Really Work?," Economics Working Papers 0055, Institute for Advanced Study, School of Social Science. [Downloadable!]
    Other versions:
  6. Mathevet, Laurent, 2007. "Supermodular Bayesian implementation: Learning and incentive design," Working Papers 1265, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  7. gunnthorsdottir, anna & vragov, roumen & mccabe, kevin & seifert, stefan, 2007. "The meritocracy as a mechanism to overcome social dilemmas," MPRA Paper 2454, University Library of Munich, Germany, revised 09 Apr 2007. [Downloadable!]
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