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

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Abstract

This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In particular, we characterize maximum and minimum revenue across all information structures when bidders may not know their own values, and maximum revenue when they do know their values. Revenue is maximized when buyers know who has the highest valuation, but the highest valuation buyer has partial information about others' values. Revenue is minimized when buyers are uncertain about whether they will win or lose and incentive constraints are binding for all upward bid deviations. We provide further analytic results on possible welfare outcomes and report computational methods which work when we do not have analytic solutions. Many of our results generalize to asymmetric value distributions. We apply these results to study how entry fees and reserve prices impact the welfare bounds.

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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 2018, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2018
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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. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2015. "The Limits of Price Discrimination," American Economic Review, American Economic Association, vol. 105(3), pages 921-957, March.
    3. Jacob Rubinstein & Elmar Wolfstetter & Michael Landsberger & Shmuel Zamir, 2001. "First-price auctions when the ranking of valuations is common knowledge," Review of Economic Design, Springer;Society for Economic Design, vol. 6(3), pages 461-480.
    4. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    5. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    6. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2013. "Extremal Information Structures in the First Price Auction," Working Papers 055-2013, Princeton University, Department of Economics, Econometric Research Program..
    7. 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.
    8. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071, December.
    9. 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.
    10. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, University of Exeter, Department of Economics.
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    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; Entry fee;
    All these keywords.

    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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