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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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  • 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
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    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. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    5. Yasuyo Hamaguchi & Satoshi Mitani & Tatsuyoshi Saijo, 2003. "Does the Varian Mechanism Work?--Emissions Trading as an Example," International Journal of Business and Economics, School of Management Development, 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. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(3), pages 441-463.
    16. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    17. Chen, Yan, 2008. "Incentive-compatible Mechanisms for Pure Public Goods: A Survey of Experimental Research," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 67, pages 625-643, Elsevier.
    18. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    19. 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.
    20. Amir, R., 1996. "Cournot oligopoly and theory of supermodular games," LIDAM Reprints CORE 1228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    21. 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.
    22. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    23. 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.
    24. repec:bla:scandj:v:81:y:1979:i:2:p:198-215 is not listed on IDEAS
    25. Yan Chen, 2002. "A family of supermodular Nash mechanisms implementing Lindahl allocations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 773-790.
    26. 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.
    27. 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.
    28. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    29. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    30. 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.
    31. 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.
    32. 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.
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    More about this item

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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