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Extremal Information Structures in the First Price Auction

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  • Dirk Bergemann
  • Benjamin A. Brooks
  • Stephen Morris

Abstract

We study how the outcomes of a private-value first price auction can vary with bidders' information, for a fixed distribution of private values. In a two bidder, two value, setting, we characterize all combinations of bidder surplus and revenue that can arise, and identify the information structure that minimizes revenue. The extremal information structure that minimizes revenue entails each bidder observing a noisy and correlated signal about the other bidder's value. In the general environment with many bidders and many values, we characterize the minimum bidder surplus of each bidder and maximum revenue across all information structures. The extremal information structure that simultaneously attains these bounds entails an efficient allocation, bidders knowing whether they will win or lose, losers bidding their true value and winners being induced to bid high by partial information about the highest losing bid. Our analysis uses a linear algebraic characterization of equilibria across all information structures, and we report simulations of properties of the set of all equilibria.
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Suggested Citation

  • Dirk Bergemann & Benjamin A. Brooks & Stephen Morris, 2014. "Extremal Information Structures in the First Price Auction," Levine's Working Paper Archive 786969000000000898, David K. Levine.
  • Handle: RePEc:cla:levarc:786969000000000898
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    References listed on IDEAS

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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. Eddie Dekel & Asher Wolinsky, 2000. "Rationalizable Outcomes of Large Independent Private-Value First Price Discrete Auctions," Discussion Papers 1308, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
    4. Hanming Fang & Stephen Morris, 2012. "Multidimensional Private Value Auctions," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 9, pages 319-356 World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
    7. 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).
    8. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    9. Dekel, Eddie & Wolinsky, Asher, 2003. "Rationalizable outcomes of large private-value first-price discrete auctions," Games and Economic Behavior, Elsevier, vol. 43(2), pages 175-188, May.
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    More about this item

    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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