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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 a ect their values before participating in the mechanism. Both the uni- form 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).

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  • 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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    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

    JEL classification:

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

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