Rent-seeking contests with independent private values

We consider symmetric rent-seeking contests with independent private valuations of the contest prize. For a two-parameter specification with continuous types, we fully characterize the Bayesian equilibrium, and study its basic properties. The willingness to waste is a hump-shaped function of the private valuation, with the median type expending the highest share of her valuation. A first-order (second-order) stochastic increase in the common type distribution raises (lowers) ex-ante expected efforts. However, neither first-order nor second-order stochastic dominance in valuations necessarily leads to a first-order stochastic dominance ranking in efforts. We also show that, as uncertainty vanishes, the Bayesian equilibrium converges to the Nash equilibrium of the model with complete information.