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

Robust Multiplicity with a Grain of Naiveté

  • Aviad Heifetz
  • Willemien Kets

In an important paper, Weinstein and Yildiz (2007) show that if players have an infinite depth of reasoning and this is commonly believed, types generically have a unique rationalizable action in games that satisfy a richness condition. We show that this result does not extend to environments where players may have a finite depth of reasoning, or think it is possible that the other player has a finite depth of reasoning, or think that the other player may think that is possible, and so on, even if this so-called "grain of naivete" is arbitrarily small. More precisely, we show that even if there is almost common belief in the event that players have an infinite depth of reasoning, there are types with multiple rationalizable actions, and the same is true for "nearby" types. Our results demonstrate that both uniqueness and multiplicity are robust phenomena when we relax the assumption that it is common belief that players have an infinite depth, if only slightly.

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.kellogg.northwestern.edu/research/math/papers/1573.pdf
File Function: main text
Download Restriction: no

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1573.

as
in new window

Length:
Date of creation: 11 Dec 2013
Date of revision:
Handle: RePEc:nwu:cmsems:1573
Contact details of provider: Postal:
Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014

Phone: 847/491-3527
Fax: 847/491-2530
Web page: http://www.kellogg.northwestern.edu/research/math/
Email:


More information through EDIRC

Order Information: Email:


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. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, 03.
  2. 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.
  3. 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.
  4. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2007. "Dynamic Global Games of Regime Change: Learning, Multiplicity, and the Timing of Attacks," Econometrica, Econometric Society, vol. 75(3), pages 711-756, 05.
  5. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on Types," Scholarly Articles 3160489, Harvard University Department of Economics.
  6. Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Giancarlo Corsetti & Amil Dasgupta & Stephen Morris & Hyun Song Shin, 2001. "Does one Soros make a difference?: a theory of currency crises with large and small traders," LSE Research Online Documents on Economics 25045, London School of Economics and Political Science, LSE Library.
  8. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
  9. Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Discussion Paper 1990-52, Tilburg University, Center for Economic Research.
  10. Pierpaolo Battigalli & Alfredo Di Tillio & Edoardo Grillo & Antonio Penta, 2008. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," Working Papers 340, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  11. Stephen Morris & Hyun Song Shin, 2004. "Liquidity Black Holes," Yale School of Management Working Papers ysm425, Yale School of Management.
  12. 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.
  13. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
  14. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2009. "Measuring Strategic Uncertainty in Coordination Games," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 181-221.
  15. Antonio Cabrales & Rosemarie Nagel & Roc Armenter, 2007. "Equilibrium selection through incomplete information in coordination games: an experimental study," Experimental Economics, Springer, vol. 10(3), pages 221-234, September.
  16. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
  17. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. 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.
  19. Ivan Werning & George-Marios Angeletos, 2005. "Crises and Prices: Information Aggregation, Multiplicity and Volatility," 2005 Meeting Papers 284, Society for Economic Dynamics.
  20. Xiong, Siyang & Chen, Yi-Chun & di Tillio, Alfredo & Faingold, Eduardo, 2010. "Uniform topologies on types," Theoretical Economics, Econometric Society, vol. 5(3), September.
  21. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
  22. Heifetz, Aviad, 1993. "The Bayesian Formulation of Incomplete Information--The Non-compact Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 329-338.
  23. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
  24. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  25. Harold L. Cole & Timothy J. Kehoe, 2000. "Self-Fulfilling Debt Crises," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 91-116.
  26. 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.
  27. Sandeep Baliga & Tomas Sjostrom, 2001. "Arms Races and Negotiations," Economics Working Papers 0007, Institute for Advanced Study, School of Social Science.
  28. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  29. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation for Research in Economics, Yale University.
  30. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  31. Willemien Kets, 2014. "Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information," Discussion Papers 1569, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  32. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2004. "The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private Information," Econometrica, Econometric Society, vol. 72(5), pages 1583-1599, 09.
  33. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2006. "Signaling in a Global Game: Coordination and Policy Traps," Journal of Political Economy, University of Chicago Press, vol. 114(3), pages 452-484, June.
  34. Itay Goldstein & Ady Pauzner, 2005. "Demand-Deposit Contracts and the Probability of Bank Runs," Journal of Finance, American Finance Association, vol. 60(3), pages 1293-1327, 06.
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:nwu:cmsems:1573. 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: (Fran Walker)

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.