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

We analyse the all-pay auction with incomplete information and variance-averse bidders. We characterise the 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 uniform valuations, we show that a more variance-averse type always bids 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. (JEL C7, D7, D81.