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

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  • Bettina Klose
  • Paul Schweinzer

Abstract

We analyse the all-pay auction with incomplete information and variance-averse bidders. We characterise the unique symmetric equilibrium for general distributions of valuations and any number of bidders. Variance aversion is a sufficient assumption to predict that high-valuation bidders increase their bids relative to the risk-neutral case while low types decrease their bid. Considering an asymmetric two-player environment with uniformly distributed valuations, we show that a variance-averse player always bids higher than her risk-neutral opponent with the same valuation. Utilising our analytically derived bidding functions we discuss all-pay auctions with variance-averse bidders from an auction designer’s perspective. We briefly consider possible extensions of our model, including noisy signals, type-dependent attitudes towards risk, and variance-seeking preferences.

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  • Bettina Klose & Paul Schweinzer, 2012. "Auctioning risk: The all-pay auction under mean-variance preferences," ECON - Working Papers 097, Department of Economics - University of Zurich, revised Dec 2017.
    • Handle: RePEc:zur:econwp:097
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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. 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).
    3. 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.
    4. 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.
    5. repec:cup:judgdm:v:11:y:2016:i:4:p:380-390 is not listed on IDEAS

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    More about this item

    Keywords

    All-pay auctions; contests; incomplete information; private values; risk-aversion; 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
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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