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First Price Auctions with General Information Structures: Implications for Bidding and Revenue

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Abstract

We explore the impact of private information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders uncertain whether they will win or lose and indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We report further analytic and computational characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from winning bid data and for the informationally robust comparison of alternative bidding mechanisms.

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  • Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2015. "First Price Auctions with General Information Structures: Implications for Bidding and Revenue," Cowles Foundation Discussion Papers 2018R, Cowles Foundation for Research in Economics, Yale University, revised Nov 2015.
  • Handle: RePEc:cwl:cwldpp:2018r
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    1. Helmuts Āzacis & Péter Vida, 2015. "Collusive communication schemes in a first-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 125-160, January.
    2. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    3. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    4. Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, January.
    5. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    6. Kim, Jinwoo & Che, Yeon-Koo, 2004. "Asymmetric information about rivals' types in standard auctions," Games and Economic Behavior, Elsevier, vol. 46(2), pages 383-397, February.
    7. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    8. 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. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Selling to Intermediaries: Optimal Auction Design in a Common Value Model," Cowles Foundation Discussion Papers 2064R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2017.
    2. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Optimal Auction Design in a Common Value Model," Cowles Foundation Discussion Papers 2064, Cowles Foundation for Research in Economics, Yale University.
    3. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    4. Carroll, Gabriel, 2016. "Informationally robust trade and limits to contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 334-361.

    More about this item

    Keywords

    First price auction; Information structure; Bayes correlated equilibrium; Private values; Interdependent values; Common values; Revenue; Surplus; Welfare bounds; Reserve price;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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