Continuity and robustness of Bayesian equilibria in Tullock contests

We show that the Bayesian equilibrium correspondence of a Tullock contest with incomplete information is upper semicontinuous. Further, we show that when equilibrium is unique and players’ costs of effort are either state independent or uniformly bounded, then it is also lower semicontinuous, and it is robust to small perturbations of the players’ information, value for the prize, and cost of effort, as well as of the contest success function.