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

Research output: Working paper

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DateIn preparation - 2012
Number of pages21
Original languageEnglish

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 all-pay 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 high-type 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.

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