Equilibrium existence in group contests of incomplete information

We prove the existence of monotone pure strategy Bayesian equilibria in group contests under individual-level and group-level private information. For the latter type, we develop a novel approach reducing group contests to contests between individuals with multi-dimensional types, with far-reaching implications for the existence and, in some cases, uniqueness of equilibrium in group contests with lottery contest success functions, both under group-level private information and complete information, and in symmetric perfectly discriminating group contests.