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Beliefs, Payoffs, Information: On the Robustness of the BDP Property in Models with Endogenous Beliefs

Author

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  • Alia Gizatulina

    (Max Planck Institute for Research on Collective Goods, Bonn)

  • Martin Hellwig

    (Max Planck Institute for Research on Collective Goods, Bonn)

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 satisfying this so-called BDP property ("beliefs determine preferences") is negligible, in a geometric and a measure-theoretic sense. In contrast, we show that, in models with finite-dimensional type spaces, this property is topologically generic if the set of objects about which beliefs are formed is sufficiently rich and beliefs are derived by conditioning on the available information; for any agent, this information includes his own payoff parameters.

Suggested Citation

  • Alia Gizatulina & Martin Hellwig, 2011. "Beliefs, Payoffs, Information: On the Robustness of the BDP Property in Models with Endogenous Beliefs," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_28, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2011_28
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    References listed on IDEAS

    as
    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. Olivier Compte & Philippe Jehiel, 2009. "Veto Constraint in Mechanism Design: Inefficiency with Correlated Types," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 182-206, February.
    3. , & , & ,, 2006. "Topologies on types," Theoretical Economics, Econometric Society, vol. 1(3), pages 275-309, September.
    4. 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.
    5. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    7. Chen, Yi-Chun & Xiong, Siyang, 2011. "The genericity of beliefs-determine-preferences models revisited," Journal of Economic Theory, Elsevier, vol. 146(2), pages 751-761, March.
    8. Allen, Beth E, 1981. "Generic Existence of Completely Revealing Equilibria for Economies with Uncertainty when Prices Convey Information," Econometrica, Econometric Society, vol. 49(5), pages 1173-1199, September.
    9. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    10. 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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    15. Yi‐Chun Chen & Siyang Xiong, 2013. "Genericity and Robustness of Full Surplus Extraction," Econometrica, Econometric Society, vol. 81(2), pages 825-847, March.
    16. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Philippe Jehiel & Konrad Mierendorff, 2021. "Auction Design with Data-Driven Misspecifications," Papers 2107.00640, arXiv.org.
    2. 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.
    3. 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.
    4. Yamashita, Takuro, 2018. "Revenue guarantees in auctions with a (correlated) common prior and additional information," TSE Working Papers 18-937, Toulouse School of Economics (TSE).
    5. 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.
    6. Alia Gizatulina & Martin Hellwig, 2015. "The Genericity of the McAfee-Reny Condition for Full Surplus Extraction in Models with a Continuum of Types," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_08, Max Planck Institute for Research on Collective Goods.

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    More about this item

    Keywords

    Mechanism Design; surplus extraction; BDP; correlated information; universal type space;
    All these keywords.

    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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