IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

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

  • Breitmoser, Yves
  • Tan, Jonathan H.W.
  • Zizzo, Daniel John

The extensive form game we study has multiple perfect equilibria, but it has a unique limiting logit equilibrium (QRE) and a unique level-k prediction as k approaches infinity. The convergence paths of QRE and level-k are different, but they converge to the same limit point. We analyze whether subjects adapt beliefs when gaining experience, and if so whether they take the QRE or the level-k learning path. We estimate transitions between level-k and QRE belief rules using Markov-switching rule learning models. The analysis reveals that subjects take the level-k learning path and that they advance gradually, switching from level 1 to 2, from level 2 to equilibrium, and reverting to level 1 after observing opponents deviating from equilibrium. The steady state therefore contains a mixture of behavioral rules: levels 0, 1, 2, and equilibrium with weights of 2.9%, 16.6%, 37.9%, and 42.6%, respectively.

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.sciencedirect.com/science/article/pii/S0899825614000463
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 86 (2014)
Issue (Month): C ()
Pages: 102-125

as
in new window

Handle: RePEc:eee:gamebe:v:86:y:2014:i:c:p:102-125
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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. Jacob K. Goeree & Charles A. Holt & Thomas R. Palfrey, 2000. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Virginia Economics Online Papers 345, University of Virginia, Department of Economics.
  2. 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.
  3. 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.
  4. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  5. Thomas Palfrey, 2002. "Quantal Response Equilibrium and Overbidding in Private Value Auctions," Theory workshop papers 357966000000000089, UCLA Department of Economics.
  6. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  7. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  8. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory Of Fairness, Competition, And Cooperation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 817-868, August.
  9. repec:kap:expeco:v:1:y:1998:i:1:p:43-62 is not listed on IDEAS
  10. Selten, Reinhard, 1996. "Axiomatic Characterization of the Quadratic Scoring Rule," Discussion Paper Serie B 390, University of Bonn, Germany.
  11. Vincent P Crawford & Nagore Iriberri, 2007. "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 321307000000001005, UCLA Department of Economics.
  12. 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.
  13. 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.
  14. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  21. 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.
  22. 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.
  23. Jacob K. Goeree & Charles A. Holt, 2000. "A Model of Noisy Introspection," Virginia Economics Online Papers 343, University of Virginia, Department of Economics.
  24. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  25. 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.
  26. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  27. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer, vol. 28(4), pages 599-615.
  28. Uri Gneezy, 2005. "Step-Level Reasoning and Bidding in Auctions," Management Science, INFORMS, vol. 51(11), pages 1633-1642, November.
  29. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
  30. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  31. 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.
  32. 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.
  33. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  34. 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.
  35. Avinash Dixit, 2003. "Clubs with Entrapment," American Economic Review, American Economic Association, vol. 93(5), pages 1824-1829, December.
  36. 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.
  37. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  38. 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.
  39. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer, vol. 30(4), pages 453-478.
  40. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
  41. 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.
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:eee:gamebe:v:86:y:2014:i:c:p:102-125. 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: (Zhang, Lei)

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.