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Beliefs, payoffs, information: On the robustness of the BDP property in models with endogenous beliefs

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  • Gizatulina, Alia
  • Hellwig, Martin

Abstract

Neeman (2004) and Heifetz and Neeman (2006) have shown that, in auctions with incomplete information about payoffs, full surplus extraction is only possible if agents’ beliefs about other agents are fully informative about their own payoff parameters. They argue that the set of incomplete-information models with common priors that satisfy this so-called BDP property (“beliefs determine preferences”) is negligible. In contrast, we show that, in models with finite-dimensional abstract type spaces, the set of belief functions with this property is topologically generic in the set of all belief functions. Our result implies genericity of (non-common or common) priors with the BDP property.

Suggested Citation

  • Gizatulina, Alia & Hellwig, Martin, 2014. "Beliefs, payoffs, information: On the robustness of the BDP property in models with endogenous beliefs," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 136-153.
  • Handle: RePEc:eee:mateco:v:51:y:2014:i:c:p:136-153
    DOI: 10.1016/j.jmateco.2013.10.010
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    References listed on IDEAS

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    1. Neeman, Zvika, 2004. "The relevance of private information in mechanism design," Journal of Economic Theory, Elsevier, vol. 117(1), pages 55-77, July.
    2. Barelli, Paulo, 2009. "On the genericity of full surplus extraction in mechanism design," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1320-1332, May.
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    6. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, January.
    7. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November.
    8. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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    12. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    13. Gizatulina, Alia & Hellwig, Martin, 2010. "Informational smallness and the scope for limiting information rents," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2260-2281, November.
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    16. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
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    Citations

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    Cited by:

    1. Sushil Bikhchandani & Ichiro Obara, 2017. "Mechanism design with information acquisition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 783-812, March.
    2. Guo, Huiyi, 2019. "Mechanism design with ambiguous transfers: An analysis in finite dimensional naive type spaces," Journal of Economic Theory, Elsevier, vol. 183(C), pages 76-105.
    3. Gizatulina, Alia & Hellwig, Martin, 2017. "The generic possibility of full surplus extraction in models with large type spaces," Journal of Economic Theory, Elsevier, vol. 170(C), pages 385-416.

    More about this item

    Keywords

    Abstract type spaces; Mechanism design; Correlated information; Belief functions; BDP property;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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