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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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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2006s-30.

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Date of creation: 01 Dec 2006
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Handle: RePEc:cir:cirwor:2006s-30

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Keywords: games; learning; experiments; stochastic fictitious play; mixed strategy equilibria; jeux; apprentissage; expériences; jeu fictif stochastique; équilibres à stratégie mixte;

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References

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  1. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
  2. 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.
  3. Ed Hopkins & Josef Hofbauer & Michel Benaim, 2005. "Learning in Games with Unstable Equilibria," ESE Discussion Papers 135, Edinburgh School of Economics, University of Edinburgh.
  4. 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.
  5. 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.
  6. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer, vol. 10(2), pages 171-178, June.
  7. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," Levine's Working Paper Archive 625018000000000226, David K. Levine.
  8. Timothy N. Cason & Daniel Friedman, 2000. "Buyer Search and Price Dispersion: A Laboratory Study," Econometric Society World Congress 2000 Contributed Papers 1549, Econometric Society.
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  10. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1999. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Virginia Economics Online Papers 332, University of Virginia, Department of Economics.
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  17. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  18. 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.
  19. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, September.
  20. 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.
  21. 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.
  22. 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.
  23. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  24. 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.
  25. 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.
  26. 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.
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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. Ed Hopkins & Josef Hofbauer & Michel Benaim, 2005. "Learning in Games with Unstable Equilibria," ESE Discussion Papers 135, Edinburgh School of Economics, University of Edinburgh.
  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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