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A Theory of Auctions With Endogenous Valuations

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  • Benny Moldovanu
  • Alex Gershkov
  • Philipp Strack

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

  • Benny Moldovanu & Alex Gershkov & Philipp Strack, 2018. "A Theory of Auctions With Endogenous Valuations," CRC TR 224 Discussion Paper Series crctr224_2018_031, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2018_031
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    Cited by:

    1. Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    2. Xu Lang, 2022. "Reduced-form budget allocation with multiple public alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 335-359, August.
    3. Wasser, Cédric & Zhang, Mengxi, 2023. "Differential treatment and the winner's effort in contests with incomplete information," Games and Economic Behavior, Elsevier, vol. 138(C), pages 90-111.
    4. Agastya, Murali & Feng, Xin & Lu, Jingfeng, 2023. "Auction design with shortlisting when value discovery is covert," Journal of Mathematical Economics, Elsevier, vol. 107(C).

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    More about this item

    Keywords

    revenue maximization; endogenous values ; investments; majorization;
    All these keywords.

    JEL classification:

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

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