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

TY - UNPB

T1 - Auctioning risk: The all-pay auction under mean-variance preferences

AU - Schweinzer, Paul

AU - Klose, Bettina

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Working paper

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

ER -