Ex ante heterogeneity in all-pay many-player auctions with Pareto distribution of costs (Q2206006)

The article is a natural development of the author's research on interesting topics: contests with many heterogeneous [\textit{S. O. Parreiras} and \textit{A. Rubinchik}, Games Econ. Behav. 68, No. 2, 703--715 (2010; Zbl 1203.91207)] and contests with stochastic abilities. In this paper the authors study an all-pay auction with risk-neutral players who have only partial information about costs of efforts of their rivals, i.e., just the lower bound of the supports of their corresponding Pareto distributions. A full characterization of the unique equilibrium of the game in terms of the profile of these lower bounds is given. The effects of heterogeneity measured as a mean-preserving spread of cost parameters of the active players are also discussed. There are two basic findings. First, as one would expect, a decrease in all cost parameters improves the outcome, be it either the maximal, minimal or the expected average effort of the active players. Second, none of the outcomes is positively related to heterogeneity of the pool of players: a mean preserving spread in cost parameters lowers the average expected effort, decreases (in terms of stochastic dominance) the minimal effort and has no effect on the distribution of the maximal effort.