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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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000898.

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Date of creation: 24 Feb 2014
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Handle: RePEc:cla:levarc:786969000000000898

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  1. Azacis, Helmuts & Vida, P├ęter, 2012. "Collusive Communication Schemes in a First-Price Auction," Cardiff Economics Working Papers E2012/11, Cardiff University, Cardiff Business School, Economics Section.
  2. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
  3. 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.
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