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On redundant types and Bayesian formulation of incomplete information

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  • Liu, Qingmin
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    Abstract

    A type structure is non-redundant if no two types of a player represent the same hierarchy of beliefs over the given set of basic uncertainties, and it is redundant otherwise. Under a mild necessary and sufficient condition termed separativity, we show that any redundant structure can be identified with a non-redundant structure with an extended space of basic uncertainties. The belief hierarchies induced by the latter structure, when "marginalized," coincide with those induced by the former. We argue that redundant structures can provide different Bayesian equilibrium predictions only because they reflect a richer set of uncertainties entertained by players but unspecified by the analyst. The analyst shall make use of a non-redundant structure, unless he believes that he misspecified the players' space of basic uncertainties. We also consider bounding the extra uncertainties by the action space for Bayesian equilibrium predictions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 144 (2009)
    Issue (Month): 5 (September)
    Pages: 2115-2145

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    Handle: RePEc:eee:jetheo:v:144:y:2009:i:5:p:2115-2145

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Incomplete information Bayesian equilibrium Redundant types Separativity;

    References

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    1. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," CORE Discussion Papers 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:
    1. Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer, vol. 46(3), pages 377-399, April.
    2. Qin, Cheng-Zhong & Yang, Chun-Lei, 2009. "An Explicit Approach to Modeling Finite-Order Type Spaces and Applications," University of California at Santa Barbara, Economics Working Paper Series qt8hq7j89k, Department of Economics, UC Santa Barbara.
    3. Tang, Qianfeng, 2010. "The Bayesian Solution and Hierarchies of Beliefs," MPRA Paper 26811, University Library of Munich, Germany.
    4. Qin, Cheng-Zhong & Yang, Chun-Lei, 2013. "Finite-order type spaces and applications," Journal of Economic Theory, Elsevier, vol. 148(2), pages 689-719.
    5. Ronald Stauber, 2013. "A Framework for Robustness to Ambiguity of Higher-Order Beliefs," ANU Working Papers in Economics and Econometrics 2013-602, Australian National University, College of Business and Economics, School of Economics.
    6. Ronald Stauber, 2014. "A framework for robustness to ambiguity of higher-order beliefs," International Journal of Game Theory, Springer, vol. 43(3), pages 525-550, August.
    7. Du, Songzi, 2012. "Correlated equilibrium and higher order beliefs about play," Games and Economic Behavior, Elsevier, vol. 76(1), pages 74-87.
    8. Tang, Qianfeng, 2010. "Interim Partially Correlated Rationalizability," MPRA Paper 26810, University Library of Munich, Germany.

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