When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting
This study clarifies the conditions under which learning in games produces convergence to Nash equilibria in practice. Previous work has identified theoretical conditions under which various stylized learning processes achieve convergence. One technical condition is supermodularity, which is closely related to the more familiar concept of strategic complementarities. We experimentally investigate the role of supermodularity in achieving convergence through learning. Using a game from the literature on solutions to externalities, we systematically vary a free parameter below, close to, at and beyond the threshold of supermodularity to assess its effects on convergence. We find that supermodular and Â¡Â°near-supermodularÂ¡Â± games converge significantly better than those far below the threshold. From a little below the threshold to the threshold, the improvement is statistically insignificant. Within the class of supermodular games, increasing the parameter far beyond the threshold does not significantly improve convergence. Simulation shows that while most experimental results persist in the long run, some become more pronounced.
|Date of creation:||Feb 2004|
|Date of revision:|
|Publication status:||published in The American Economic Review, 94(5), December 2004, 1505Â–1503.|
|Contact details of provider:|| Postal: Williamstown, MA 01267|
Phone: 413 597 2476
Fax: 413 597 4045
Web page: http://econ.williams.edu
More information through EDIRC
|Order Information:|| Email: |
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.:
- 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.
- John B Van Huyck & Raymond C Battalio & Richard O Beil, 1997. "Tacit coordination games, strategic uncertainty, and coordination failure," Levine's Working Paper Archive 1225, David K. Levine.
- J. B. Van Huyck & R. C. Battalio & R. O. Beil, 2010. "Tacit coordination games, strategic uncertainty, and coordination failure," Levine's Working Paper Archive 661465000000000393, David K. Levine.
- 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.
- Ronald M. Harstad & Michael Marrese, 1980.
"Behavioral Explanations of Efficient Public Good Allocations,"
422, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
- Dybvig, Philip H. & Spatt, Chester S., 1983. "Adoption externalities as public goods," Journal of Public Economics, Elsevier, vol. 20(2), pages 231-247, March.
- Diamond, Peter A, 1982.
"Aggregate Demand Management in Search Equilibrium,"
Journal of Political Economy,
University of Chicago Press, vol. 90(5), pages 881-94, October.
- Chen, Yan & Khoroshilov, Yuri, 2003. "Learning under limited information," Games and Economic Behavior, Elsevier, vol. 44(1), pages 1-25, July.
- Hal R. Varian, 1994.
"A Solution to the Problem of Externalities when Agents are Well-Informed},"
- 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 1278-93, December.
- Varian, H,R., 1991. "A Solution to the Problem of Externalities when Agents are Well-Informed," Papers 10, Michigan - Center for Research on Economic & Social Theory.
- 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.
- Vives, X., 1988.
"Nash Equilibrium With Strategic Complementarities,"
UFAE and IAE Working Papers
107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- Yasuyo Hamaguchi & Satoshi Mitani & Tatsuyoshi Saijo, 2004.
"Does the Varian Mechanism Work? -Emissions Trading as an Example,"
04009, Research Institute of Economy, Trade and Industry (RIETI).
- 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.
- AMIR, Rabah, 1994.
"Cournot Oligopoly and the Theory of Supermodular Games,"
CORE Discussion Papers
1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
- Boylan, Richard T. & El-Gamal, Mahmoud A., 1990.
"Fictitious Play: A Statistical Study of Multiple Economic Experiments,"
737, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- R. Boylan & E. El-Gamal, 2010. "Fictitious Play: A Statistical Study of Multiple Economic Experiments," Levine's Working Paper Archive 403, David K. Levine.
- 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.
- 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.
- 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.
- 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.
- Douglas W. Diamond & Philip H. Dybvig, 2000.
"Bank runs, deposit insurance, and liquidity,"
Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
- 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.
- 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.
- Josef Falkinger & Ernst Fehr & Simon Gaechter, . "A Simple Mechanism for the Efficient Provision of Public Goods - Experimental Evidence," IEW - Working Papers 003, Institute for Empirical Research in Economics - University of Zurich.
- Chen, Yan, 2008. "Incentive-compatible Mechanisms for Pure Public Goods: A Survey of Experimental Research," Handbook of Experimental Economics Results, Elsevier.
- Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
- Jasmina Arifovic & John Ledyard, 2002. "Computer Testbeds and Mechanism Design," Computing in Economics and Finance 2002 262, Society for Computational Economics.
- 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.
- 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.
- Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
- 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.
- Andreoni,J. & Varian,H., 1999. "Pre-play contracting in the prisoners' dilemma," Working papers 18, Wisconsin Madison - Social Systems.
When requesting a correction, please mention this item's handle: RePEc:wil:wileco:2004-02. 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: (Stephen Sheppard)
If references are entirely missing, you can add them using this form.