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On the beliefs off the path: Equilibrium refinement due to quantal response and level-k

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  • Yves Breitmoser

    (Department of Economics, EUV Frankfurt (Oder))

  • Jonathan H. W. Tan

    (Nottingham University Business School)

  • Daniel John Zizzo

    (School of Economics and CBESS, University of East Anglia)

Abstract

This paper studies the relevance of equilibrium and nonequilibrium explanations of behavior, with respects to equilibrium refinement, as players gain experience. We investigate this experimentally using an incomplete information sequential move game with heterogeneous preferences and multiple perfect equilibria. Only the limit point of quantal response (the limiting logit equilibrium), and alternatively that of level-k reasoning (extensive form rationalizability), restricts beliefs off the equilibrium path. Both concepts converge to the same unique equilibrium, but the predictions differ prior to convergence. We show that with experience of repeated play in relatively constant environments, subjects approach equilibrium via the quantal response learning path. With experience spanning also across relatively novel environments, though, level-k reasoning tends to dominate.

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Bibliographic Info

Paper provided by School of Economics, University of East Anglia, Norwich, UK. in its series Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) with number 10-05.

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Date of creation: 01 Mar 2010
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Handle: RePEc:uea:wcbess:10-05

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Postal: Helen Chapman, School of Economics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK
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Related research

Keywords: incomplete information; equilibrium refinement; logit equilibrium; rationalizability; quantal response; level-k; inequity aversion; experiment;

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  1. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  2. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
  3. Ho, Teck Hua & Weigelt, Keith & Camerer, Colin, 1996. "Iterated Dominance and Iterated Best-Response in Experimental P-Beauty Contests," Working Papers 974, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. David J Cooper & John B Van Huyck, 2002. "Evidence on the Equivalence of the Stratetic and Extensive Form Representation of Games," Levine's Working Paper Archive 234936000000000001, David K. Levine.
  5. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers 11920, Iowa State University, Department of Economics.
  6. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  7. Stahl, Dale O., 1998. "Is step-j thinking an arbitrary modelling restriction or a fact of human nature?," Journal of Economic Behavior & Organization, Elsevier, vol. 37(1), pages 33-51, September.
  8. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  9. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  10. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
  11. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1998. "Rent Seeking with Bounded Rationality: An Analysis of the All-Pay Auction," Journal of Political Economy, University of Chicago Press, vol. 106(4), pages 828-853, August.
  12. Alejandro Gaviria & Steven Raphael, 2001. "School-Based Peer Effects And Juvenile Behavior," The Review of Economics and Statistics, MIT Press, vol. 83(2), pages 257-268, May.
  13. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
  14. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  15. Crawford, Vincent P. & Iriberri, Nagore, 2005. "Level-k Auctions: Can a Non-Equilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," University of California at San Diego, Economics Working Paper Series qt12586197, Department of Economics, UC San Diego.
  16. Ernst Fehr & Klaus M. Schmidt, . "A Theory of Fairness, Competition and Cooperation," IEW - Working Papers 004, Institute for Empirical Research in Economics - University of Zurich.
  17. repec:kap:expeco:v:1:y:1998:i:1:p:43-62 is not listed on IDEAS
  18. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
  19. 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.
  20. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer, vol. 30(4), pages 453-478.
  21. Camerer, Colin F. & Palfrey, Thomas R. & Rogers, Brian W., 2006. "Heterogeneous quantal response equilibrium and cognitive hierarchies," Working Papers 1260, California Institute of Technology, Division of the Humanities and Social Sciences.
  22. Kuran, Timur, 1998. "Ethnic Norms and Their Transformation through Reputational Cascades," The Journal of Legal Studies, University of Chicago Press, vol. 27(2), pages 623-59, June.
  23. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  24. Goeree, Jacob K. & Holt, Charles A., 2004. "A model of noisy introspection," Games and Economic Behavior, Elsevier, vol. 46(2), pages 365-382, February.
  25. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  26. Palfrey, Thomas R. & Goeree, Jacob & Holt, Charles, 2000. "Quantal Response Equilibrium and Overbidding in Private-value Auctions," Working Papers 1073, California Institute of Technology, Division of the Humanities and Social Sciences.
  27. Stahl, Dale O. & Haruvy, Ernan, 2008. "Level-n bounded rationality in two-player two-stage games," Journal of Economic Behavior & Organization, Elsevier, vol. 65(1), pages 41-61, January.
  28. Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - Center for Economic Research.
  29. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  30. Turocy, Theodore L., 2005. "A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence," Games and Economic Behavior, Elsevier, vol. 51(2), pages 243-263, May.
  31. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, MIT Press, vol. 119(3), pages 861-898, August.
  32. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  33. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  34. Dorothea Kübler & Georg Weizs�cker, 2004. "Limited Depth of Reasoning and Failure of Cascade Formation in the Laboratory," Review of Economic Studies, Oxford University Press, vol. 71(2), pages 425-441.
  35. Uri Gneezy, 2005. "Step-Level Reasoning and Bidding in Auctions," Management Science, INFORMS, vol. 51(11), pages 1633-1642, November.
  36. Daniel L. McFadden, 1976. "Quantal Choice Analaysis: A Survey," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 363-390 National Bureau of Economic Research, Inc.
  37. Thomas Palfrey, 2002. "Quantal Response Equilibrium and Overbidding in Private Value Auctions," Theory workshop papers 357966000000000089, UCLA Department of Economics.
  38. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer, vol. 28(4), pages 599-615.
  39. Selten, Reinhard, 1996. "Axiomatic Characterization of the Quadratic Scoring Rule," Discussion Paper Serie B 390, University of Bonn, Germany.
  40. Avinash Dixit, 2003. "Clubs with Entrapment," American Economic Review, American Economic Association, vol. 93(5), pages 1824-1829, December.
  41. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
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