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A Theory of Auctions with Endogenous Valuations

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  • Moldovanu, Benny

Abstract

We study the revenue maximizing allocation of m units among n symmetric agents that have unit demand and convex preferences over the probability of receiving an object. Such preferences are naturally induced by a game where the agents take costly actions that affect their values before participating in the mechanism. Both the uniform m + 1 price auction and the discriminatory pay-your-bid auction with reserve prices constitute symmetric revenue maximizing mechanisms. Contrasting the case with linear preferences, the optimal reserve price reacts to both demand and supply, i.e., it depends both on the number of objects m and on number of agents n. The main tool in our analysis is an integral inequality involving majorization, super-modularity and convexity due to Fan and Lorentz (1954).

Suggested Citation

  • Moldovanu, Benny, 2018. "A Theory of Auctions with Endogenous Valuations," CEPR Discussion Papers 13259, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:13259
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    References listed on IDEAS

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    1. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
    2. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    3. Celik Gorkem & Yilankaya Okan, 2009. "Optimal Auctions with Simultaneous and Costly Participation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-33, July.
    4. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    5. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
    6. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
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    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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