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A Framework for Robustness to Ambiguity of Higher-Order Beliefs

  • Ronald Stauber

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    This paper defines simple procedures to construct ambiguous perturbations of belief structures associated to standard type spaces with precise beliefs, based on ambiguous type spaces whose induced belief hierarchies approximate the belief hierarchies corresponding to the initial type space. Two alternative procedures to construct such perturbations are introduced, and are shown to yield a simple and intuitive characterization of convergence of the resulting approximations to the initial unperturbed environment. The perturbations arising from one of these procedures include the set of all finite perturbations as a special case. The introduced perturbations and their convergence properties provide a foundation for the analysis of robustness to ambiguity of various solutions concepts, and for various decision rules under ambiguity.

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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp602.pdf
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    Paper provided by Australian National University, College of Business and Economics, School of Economics in its series ANU Working Papers in Economics and Econometrics with number 2013-602.

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    Length: 29 Pages
    Date of creation: Feb 2013
    Date of revision:
    Handle: RePEc:acb:cbeeco:2013-602
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    1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    2. Bergemann, Dirk & Schlag, Karl, 2011. "Robust monopoly pricing," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2527-2543.
    3. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on Types," Scholarly Articles 3160489, Harvard University Department of Economics.
    4. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
    5. Bose, Subir & Ozdenoren, Emre & Pape, Andreas, 2006. "Optimal auctions with ambiguity," Theoretical Economics, Econometric Society, vol. 1(4), pages 411-438, December.
    6. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    7. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer, vol. 46(3), pages 377-399, April.
    8. 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.
    9. Subir Bose & Arup Daripa, 2008. "A Dynamic Mechanism and Surplus Extraction Under Ambiguity," Discussion Papers in Economics 08/24, Department of Economics, University of Leicester.
    10. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
    11. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    12. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2004. "Search and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 119(2), pages 299-333, December.
    13. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    14. Atsushi Kajii & Takashi Ui, 2004. "Incomplete Information Games with Multiple Priors," KIER Working Papers 583, Kyoto University, Institute of Economic Research.
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