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A Simple Test of Learning Theory

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  • Jim Engle-Warnick
  • Ed Hopkins

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. Nous faisons le compte rendu d'expériences élaborées afin de tester la possibilité théorique, découverte par Shapley (1964), que dans certains jeux, l'apprentissage ne converge pas vers un équilibre, que ce soit en termes de fréquences marginales ou de jeu moyen. Les sujets ont joué à répétition en paires fixes à un de deux jeux 3 ´ 3, chaque jeu ayant un équilibre de Nash unique avec stratégies mixtes. On prévoit que l'équilibre du premier jeu soit stable après apprentissage, et le deuxième jeu instable, à condition que les gains soient suffisamment élevés. Pour chaque jeu, nous avons eu recours à deux différents traitements : un avec gains faibles et l'autre avec gains élevés. Nous avons constaté que dans tous les traitements, le jeu moyen est près de l'équilibre bien qu'il y ait présence de cycles importants dans les données.
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Suggested Citation

  • Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," CIRANO Working Papers 2006s-30, CIRANO.
  • Handle: RePEc:cir:cirwor:2006s-30
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    File URL: https://cirano.qc.ca/files/publications/2006s-30.pdf
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    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. 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.
    3. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, Decembrie.
    4. 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.
    5. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    6. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    7. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    8. Cason, Timothy N. & Friedman, Daniel, 2003. "Buyer search and price dispersion: a laboratory study," Journal of Economic Theory, Elsevier, vol. 112(2), pages 232-260, October.
    9. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    10. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    11. 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.
    12. 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.
    13. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    14. 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.
    15. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November.
    16. Duffy, John & Hopkins, Ed, 2005. "Learning, information, and sorting in market entry games: theory and evidence," Games and Economic Behavior, Elsevier, vol. 51(1), pages 31-62, April.
    17. 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.
    18. 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 848-881, September.
    19. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
    20. 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 749-764, May.
    21. 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.
    22. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, John Wiley & Sons, vol. 69(1), pages 21-47, July.
    23. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, John Wiley & Sons, vol. 69(1), pages 21-47, July.
    24. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    25. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    26. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    27. 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.
    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 1065-1081, September.
    29. 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.
    30. 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.
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    Cited by:

    1. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    2. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed, 2010. "Testing the TASP: An experimental investigation of learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2309-2331, November.
    3. García-Gallego, Aurora & Georgantzís, Nikolaos & Jaramillo-Gutiérrez, Ainhoa & Pereira, Pedro & Pernías-Cerrillo, J. Carlos, 2014. "On the evolution of monopoly pricing in Internet-assisted search markets," Journal of Business Research, Elsevier, vol. 67(5), pages 795-801.
    4. Jim Engle-Warnick, 2007. "Five Indefinitely Repeated Games in the Laboratory," CIRANO Working Papers 2007s-11, CIRANO.

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    More about this item

    Keywords

    games; learning; experiments; stochastic fictitious play; mixed strategy equilibria; jeux; apprentissage; expériences; jeu fictif stochastique; équilibres à stratégie mixte;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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