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

Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information

  • Willemien Kets

The standard framework for analyzing games with incomplete information models players as if they have an infinite depth of reasoning, which is not always consistent with experimental evidence. This paper generalizes the type spaces of Harsanyi (1967- 1968) so that players can have a nite depth of reasoning. We do this restricting the set of events that a player of a finite depth can reason about. This approach allows us to extend the Bayesian-Nash equilibrium concept to environments with players with a nite depth of reasoning. We demonstrate that the standard approach of modeling beliefs with Harsanyi type spaces fails to capture the equilibrium behavior of players with a nite depth, at least in some games. Consequently, the standard approach cannot be used to describe the equilibrium behavior of players with a finite depth in general.

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/1569.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 1569.

as
in new window

Length:
Date of creation: 07 Feb 2014
Date of revision:
Handle: RePEc:nwu:cmsems:1569
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. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
  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. Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
  5. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Topologies on Types," Harvard Institute of Economic Research Working Papers 2093, Harvard - Institute of Economic Research.
  6. Broseta, Bruno & Costa-Gomes, Miguel & Crawford, Vincent P., 2000. "Cognition and Behavior in Normal-Form Games: An Experimental Study," University of California at San Diego, Economics Working Paper Series qt0fp8278k, Department of Economics, UC San Diego.
  7. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Eddie Dekel & Drew Fudenberg & David K. Levine, 2000. "Learning to Play Bayesian Games," Discussion Papers 1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001.
  9. 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.
  10. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  11. Strzalecki, Tomasz, 2014. "Depth of Reasoning and Higher Order Beliefs," Scholarly Articles 14397608, Harvard University Department of Economics.
  12. 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.
  13. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  14. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-69, September.
  15. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
  16. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
  17. 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.
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:1569. 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.