An equilibrium characterization of an all-pay auction with certain and uncertain prizes

In the important contribution “All pay auctions with certain and uncertain prizes” published in Minchuk and Sela (2014), the authors analyze an all pay auction with multiple prizes. The specific feature of the model is that all valuations are common except for the valuation of one of the prizes, for which contestants have private valuations. However, the equilibrium characterization derived in the paper is incorrect. This paper provides the correct equilibrium characterization of the model.