IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

On the Beliefs off the Path: Equilibrium Refinement due to Quantal Response and Level-k

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.nottingham.ac.uk/~lizecon/RePEc/bbr/pdf/9.pdf
Download Restriction: no

Paper provided by International Centre for Behavioural Business Research in its series ICBBR Working Papers with number 9.

as
in new window

Length:
Date of creation: 17 Mar 2010
Handle: RePEc:bbr:workpa:9
Contact details of provider: Postal:
Jubilee Campus, Nottingham NG2 8BB

Phone: +44-115-846 66 02
Fax: +44-115-846 66 67
Web page: http://www.nottingham.ac.uk/business/
Email:


More information through EDIRC

References listed on IDEAS
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.:

as
in new window

  1. Costa-Gomes, Miguel & Crawford, Vincent P. & Broseta, Bruno, 1998. "Cognition and Behavior in Normal-Form Games: An Experimental Study," University of California at San Diego, Economics Working Paper Series qt1vn4h7x5, Department of Economics, UC San Diego.
  2. Vincent P. Crawford & Nagore Iriberri, 2006. "Level-k Auctions: Can a Non-Equilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Levine's Bibliography 321307000000000256, UCLA Department of Economics.
  3. Ernst Fehr & Klaus M. Schmidt, "undated". "A Theory of Fairness, Competition and Cooperation," IEW - Working Papers 004, Institute for Empirical Research in Economics - University of Zurich.
  4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
  5. Miguel A. Costa-Gomes & Vincent P. Crawford, 2004. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," ISER Discussion Paper 0613, Institute of Social and Economic Research, Osaka University.
  6. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, Oxford University Press, vol. 119(3), pages 861-898.
  7. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  8. 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.
  9. Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
  10. Thomas Palfrey, 2002. "Quantal Response Equilibrium and Overbidding in Private Value Auctions," Theory workshop papers 357966000000000089, UCLA Department of Economics.
  11. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
  12. 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.
  13. Atsushi Kajii & Stephen Morris, "undated". "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  14. Kyle Hyndman & Erkut Y. Ozbay & Andrew Schotter & Wolf Ze’ev Ehrblatt, 2012. "Convergence: An Experimental Study Of Teaching And Learning In Repeated Games," Journal of the European Economic Association, European Economic Association, vol. 10(3), pages 573-604, 05.
  15. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers Archive 11920, Iowa State University, Department of Economics.
  16. 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.
  17. 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.
  18. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
  19. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
  20. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
  21. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  22. Dale O. Stahl, 1997. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," CARE Working Papers 9710, The University of Texas at Austin, Center for Applied Research in Economics.
  23. Johnson, Eric J. & Camerer, Colin & Sen, Sankar & Rymon, Talia, 2002. "Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining," Journal of Economic Theory, Elsevier, vol. 104(1), pages 16-47, May.
  24. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
  25. 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.
  26. Dale O. Stahl & Paul W. Wilson, 2010. "On Players' Models of Other Players: Theory and Experimental Evidence," Levine's Working Paper Archive 542, David K. Levine.
  27. Kawagoe, Toshiji & Takizawa, Hirokazu, 2009. "Equilibrium refinement vs. level-k analysis: An experimental study of cheap-talk games with private information," Games and Economic Behavior, Elsevier, vol. 66(1), pages 238-255, May.
  28. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 453-478.
  29. 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.
  30. Jacob K. Goeree & Charles A. Holt, 2000. "A Model of Noisy Introspection," Virginia Economics Online Papers 343, University of Virginia, Department of Economics.
  31. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  32. repec:kap:expeco:v:1:y:1998:i:1:p:43-62 is not listed on IDEAS
  33. Uri Gneezy, 2005. "Step-Level Reasoning and Bidding in Auctions," Management Science, INFORMS, vol. 51(11), pages 1633-1642, November.
  34. Kuran, Timur, 1998. "Ethnic Norms and Their Transformation through Reputational Cascades," The Journal of Legal Studies, University of Chicago Press, vol. 27(2), pages 623-659, June.
  35. 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.
  36. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
  37. Avinash Dixit, 2003. "Clubs with Entrapment," American Economic Review, American Economic Association, vol. 93(5), pages 1824-1829, December.
  38. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
  39. 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.
  40. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  41. Dorothea Kübler & Georg Weizsäcker, 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.
  42. 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.
  43. 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.
  44. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  45. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
  46. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
  47. 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.
  48. 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.
  49. Haruvy, Ernan & Stahl, Dale O., 2012. "Between-game rule learning in dissimilar symmetric normal-form games," Games and Economic Behavior, Elsevier, vol. 74(1), pages 208-221.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:bbr:workpa:9. 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: (Laure Cabantous)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.