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.
Highlights
In economic contests players make irrecoverable investments in order to increase their chances of winning a prize
Corollary 1 shows that the comparative statics of equilibrium bidding in the number of participants in an all-pay auction qualitatively do not differ whether bidders are risk neutral or symmetrically variance-averse
We have shown that in the all-pay auction consideration of variance aversion generates the commonly observed bidding behaviour, which is often attributed to risk aversion
Summary
In economic contests players make irrecoverable investments in order to increase their chances of winning a prize. We attempt to close the aforementioned gap in the literature by characterising optimal bidding and revenue-maximizing selling behaviour in the all-pay auction with private values and variance-averse bidders This auction type may be viewed as a natural candidate for an analysis that incorporates attitudes towards risk because it exposes a bidder to the inherent risk of either winning the object (potentially at a bargain) or losing one’s bid without gaining anything. Employing mean-variance preferences—with the understanding that these will closely approximate expected utility maximisation for a large class of von-Neumann-Morgenstern utility functions— allows us to derive closed form solutions for the equilibrium bidding functions These can be used to perform comparative statics and analyse revenue
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