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Auctioning risk: The all-pay auction under mean-variance preferences

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  • Bettina Klose
  • Paul Schweinzer
Abstract
We develop the idea of using mean-variance preferences for the analysis of the first-price, all-pay auction. On the bidding side, we characterise the optimal strategy in symmetric allpay auctions under mean-variance preferences for general distributions of valuations and any number of bidders. We find that, in contrast to winner-pay auction formats, only hightype bidders increase their bids relative to the risk-neutral case while low types minimise variance exposure by bidding low. Introducing asymmetric variance aversions across bidders into a Uniform valuations, two-player framework, we show that a more variance-averse type bids always higher than her less variance-averse counterpart. Taking mean-variance bidding behaviour as given, we show that an expected revenue maximising seller may want to optimally limit the number of participants. Although expected revenue for risk-neutral bidders typically dominates revenue under mean-variance bidding, if the seller himself takes account of the variance of revenue, he may find it preferable to attract bidders endowed with mean-variance preferences.

Suggested Citation

  • Bettina Klose & Paul Schweinzer, 2012. "Auctioning risk: The all-pay auction under mean-variance preferences," Discussion Papers 12/32, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:12/32
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    Cited by:

    1. Fu, Qiang & Wang, Xiruo & Wu, Zenan, 2021. "Multi-prize contests with risk-averse players," Games and Economic Behavior, Elsevier, vol. 129(C), pages 513-535.
    2. Einav Hart & Judith Avrahami & Yaakov Kareev, 2016. "Enlarging the market yet decreasing the profit: An experimental study of competitive behavior when investment affects the prize," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 11(4), pages 380-390, July.
    3. repec:cup:judgdm:v:11:y:2016:i:4:p:380-390 is not listed on IDEAS
    4. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2022. "On equilibrium existence in generalized multi-prize nested lottery contests," Journal of Economic Theory, Elsevier, vol. 200(C).
    5. Chen, Zhuoqiong (Charlie) & Ong, David & Segev, Ella, 2017. "Heterogeneous risk/loss aversion in complete information all-pay auctions," European Economic Review, Elsevier, vol. 95(C), pages 23-37.

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    More about this item

    Keywords

    Auctions; Contests; Mean-Variance preferences;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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