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

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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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File URL: http://cowles.yale.edu/sites/default/files/files/pub/d20/d2018-r.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 2018R.

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Length: 65 pages
Date of creation: Aug 2015
Date of revision: Nov 2015
Handle: RePEc:cwl:cwldpp:2018r
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Web page: http://cowles.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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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, 01.
  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, "undated". "Five legitimate definitions of correlated equilibrium in games with incomplete informations," CORE Discussion Papers RP 1071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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