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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: http://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. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing," Cowles Foundation Discussion Papers 1527R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2007.
    2. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    3. Andreas Pape & Subir Bose & Emre Ozdenoren, 2004. "Optimal auctions with ambiguity," Econometric Society 2004 North American Summer Meetings 609, Econometric Society.
    4. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
    5. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
    6. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on types," Theoretical Economics, Econometric Society, vol. 1(3), pages 275-309, 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. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. 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.
    11. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2004. "Search and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 119(2), pages 299-333, December.
    12. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    13. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    14. 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.
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