IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

A framework for robustness to ambiguity of higher-order beliefs

  • Ronald Stauber


Registered author(s):

    Standard type spaces induce belief structures defined by precise beliefs. This paper proposes and analyzes simple procedures for constructing perturbations of such belief structures in which beliefs have a degree of ambiguity. Specifically, we construct ambiguous type spaces whose induced (ambiguous) belief hierarchies approximate the standard, precise, belief hierarchies corresponding to the initial type space. Based on a metric that captures the resulting approximation, two alternative procedures to construct such perturbations are introduced, and are shown to yield a simple and intuitive characterization of convergence to the initial unperturbed environment. As a special case, one of these procedures is shown to characterize the set of all finite perturbations. The introduced perturbations and their convergence properties provide conceptual foundations for the analysis of robustness to ambiguity of various solutions concepts, and for various decision rules under ambiguity. Copyright Springer-Verlag Berlin Heidelberg 2014

    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:
    Download Restriction: Access to full text is restricted to subscribers.

    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 Springer in its journal International Journal of Game Theory.

    Volume (Year): 43 (2014)
    Issue (Month): 3 (August)
    Pages: 525-550

    in new window

    Handle: RePEc:spr:jogath:v:43:y:2014:i:3:p:525-550
    Contact details of provider: Web page:

    Order Information: Web:

    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. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    2. Anonymous, 2006. "List of Papers 2006," 2006 Conference, August 24-25, 2006, Nelson, New Zealand 31955, New Zealand Agricultural and Resource Economics Society.
    3. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
    4. Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
    5. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    6. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    7. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on Types," Scholarly Articles 3160489, Harvard University Department of Economics.
    8. Dirk Bergemann & Karl Schlag, 2007. "Robust Monopoly Pricing," Levine's Bibliography 321307000000000983, UCLA Department of Economics.
    9. 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.
    10. Takahashi, Satoru & Chassang, Sylvain, 2011. "Robustness to incomplete information in repeated games," Theoretical Economics, Econometric Society, vol. 6(1), January.
    11. Andreas Pape & Subir Bose & Emre Ozdenoren, 2004. "Optimal auctions with ambiguity," Econometric Society 2004 North American Summer Meetings 609, Econometric Society.
    12. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2004. "Search and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 119(2), pages 299-333, December.
    13. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer, vol. 46(3), pages 377-399, April.
    14. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351.
    15. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, 03.
    16. Subir Bose & Arup Daripa, 2007. "A Dynamic Mechanism and Surplus Extraction Under Ambiguity," Birkbeck Working Papers in Economics and Finance 0716, Birkbeck, Department of Economics, Mathematics & Statistics.
    17. Anonymous, 2006. "List of Papers 2006," 2006 Conference, August 24-25, 2006, Nelson, New Zealand 31955, New Zealand Agricultural and Resource Economics Society.
    18. Oyama, Daisuke & Tercieux, Olivier, 2005. "Robust Equilibria under Non-Common Priors," MPRA Paper 14287, University Library of Munich, Germany.
    19. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
    20. Anonymous, 2006. "Selected Papers, Annual Meetings (Abstracts)," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 38(02), August.
    21. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    22. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
    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:spr:jogath:v:43:y:2014:i:3:p:525-550. 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: (Sonal Shukla)

    or (Christopher F Baum)

    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.