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English auctions with ensuing risks and heterogeneous bidders

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  • Hu, Audrey
  • Matthews, Steven A.
  • Zou, Liang

Abstract

We establish conditions under which an English auction for an indivisible risky asset has an efficient ex post equilibrium when the bidders are heterogeneous in both their exposures to, and their attitudes toward, the ensuing risk the asset will generate for the winning bidder. Each bidder’s privately known type may affect both his risk attitude and the expected value of the asset’s return to the winner. An ex post equilibrium in which the winning bidder has the largest willingness to pay for the asset exists if two conditions hold: each bidder’s marginal utility of income is log-supermodular, and the vector-valued function mapping the type vector into the bidders’ expected values for the asset satisfies a weighted average crossing condition. However, this equilibrium need not be efficient. We show that it is efficient if each bidder’s expected value for the asset is nonincreasing in the types of the other bidders, or if the bidders exhibit nonincreasing absolute risk aversion, or if the asset is riskless.

Suggested Citation

  • Hu, Audrey & Matthews, Steven A. & Zou, Liang, 2018. "English auctions with ensuing risks and heterogeneous bidders," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 33-44.
    • Handle: RePEc:eee:mateco:v:76:y:2018:i:c:p:33-44
    DOI: 10.1016/j.jmateco.2018.02.002
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    References listed on IDEAS

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    1. Péter Esö & Lucy White, 2004. "Precautionary Bidding in Auctions," Econometrica, Econometric Society, vol. 72(1), pages 77-92, January.
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    5. Dubra, Juan & Echenique, Federico & Manelli, Alejandro M., 2009. "English auctions and the Stolper-Samuelson theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 825-849, March.
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    Cited by:

    1. Hu, Audrey & Zou, Liang, 2015. "Sequential auctions, price trends, and risk preferences," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 319-335.
    2. Audrey Hu & Liang Zou, 2016. "Sequential Auctions with Generalized Interdependent Values," Tinbergen Institute Discussion Papers 16-016/I, Tinbergen Institute.
    3. Baisa, Brian, 2020. "Efficient multi-unit auctions for normal goods," Theoretical Economics, Econometric Society, vol. 15(1), January.
    4. Vasserman, Shoshana & Watt, Mitchell, 2021. "Risk aversion and auction design: Theoretical and empirical evidence," International Journal of Industrial Organization, Elsevier, vol. 79(C).

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    More about this item

    Keywords

    English auction; Ensuing risk; Heterogeneous risk preferences; Interdependent values; Ex post equilibrium; Ex post efficiency;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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