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A Simple Test of Learning Theory?

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  • Jim Engle-Warnick
  • Ed Hopkins

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Abstract

We report experiments designed to test the theoretical possibility, first discovered by Shapley (1964), that in some games learning fails to converge to any equilibrium, either in terms of marginal frequencies or of average play. Subjects played repeatedly in fixed pairings one of two 3 × 3 games, each having a unique Nash equilibrium in mixed strategies. The equilibrium of one game is predicted to be stable under learning, the other unstable, provided payoffs are sufficiently high. We ran each game in high and low payoff treatments. We find that, in all treatments, average play is close to equilibrium even though there are strong cycles present in the data.

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File URL: http://www.econ.ed.ac.uk/papers/simplecompletedec2006.pdf
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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 153.

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Length: 29
Date of creation: Dec 2006
Date of revision:
Handle: RePEc:edn:esedps:153

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Related research

Keywords: : Games; Learning; Experiments; Stochastic Fictitious Play; Mixed Strategy Equilibria.;

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References

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  1. Ed Hopkins & Robert M Seymour, 2004. "The Stability of Price Dispersion under Seller and Consumer Learning," ESE Discussion Papers 52, Edinburgh School of Economics, University of Edinburgh.
  2. Cason, Timothy N. & Friedman, Daniel & Wagener, Florian, 2005. "The dynamics of price dispersion, or Edgeworth variations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 801-822, April.
  3. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  4. 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.
  5. Timothy N. Cason & Daniel Friedman, 2000. "Buyer Search and Price Dispersion: A Laboratory Study," Econometric Society World Congress 2000 Contributed Papers 1549, Econometric Society.
  6. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-64, May.
  7. John Duffy & Ed Hopkins, 2004. "Learning, Information and Sorting in Market Entry Games: Theory and Evidence," ESE Discussion Papers 78, Edinburgh School of Economics, University of Edinburgh.
  8. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
  9. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  10. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
  11. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2006. "Learning in Games with Unstable Equilibria," Levine's Bibliography 321307000000000547, UCLA Department of Economics.
  12. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
  13. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  14. Ed Hopkins, 2004. "Two Competing Models of How People Learn in Games," ESE Discussion Papers 51, Edinburgh School of Economics, University of Edinburgh.
  15. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  16. Michael R. Baye & John Morgan, 2001. "Information Gatekeepers on the Internet and the Competitiveness of Homogeneous Product Markets," American Economic Review, American Economic Association, vol. 91(3), pages 454-474, June.
  17. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
  18. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer, vol. 10(2), pages 171-178, June.
  19. Tang, Fang-Fang, 2001. "Anticipatory learning in two-person games: some experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 44(2), pages 221-232, February.
  20. Glenn Ellison & Drew Fudenberg, 1998. "Learning Purified Mixed Equilibria," Harvard Institute of Economic Research Working Papers 1817, Harvard - Institute of Economic Research.
  21. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
  22. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, Southern Economic Association, vol. 69(1), pages 21-47, July.
  23. Morgan, John & Orzen, Henrik & Sefton, Martin, 2006. "An experimental study of price dispersion," Games and Economic Behavior, Elsevier, vol. 54(1), pages 134-158, January.
  24. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  25. Van Huyck, John B & Cook, Joseph P & Battalio, Raymond C, 1994. "Selection Dynamics, Asymptotic Stability, and Adaptive Behavior," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 975-1005, October.
  26. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2003. "Risk averse behavior in generalized matching pennies games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 97-113, October.
  27. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
  28. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-81, September.
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Cited by:
  1. Cason, Timothy N. & Friedman, Daniel UC & Hopkins, Ed, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," SIRE Discussion Papers 2009-15, Scottish Institute for Research in Economics (SIRE).
  2. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2005. "Learning in Games with Unstable Equilibria," Levine's Bibliography 784828000000000609, UCLA Department of Economics.
  3. Jim Engle-Warnick, 2007. "Five Indefinitely Repeated Games in the Laboratory," CIRANO Working Papers 2007s-11, CIRANO.
  4. Aurora García-Gallego & Nikolaos Georgantzis & Ainhoa Jaramillo-Gutiérrez & Pedro Pereira & J. Carlos Pernías-Cerrillo, 2013. "On the evolution of monopoly pricing in Internet-assisted search markets," Working Papers 2013/05, Economics Department, Universitat Jaume I, Castellón (Spain).

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