Rent-seeking group contests with one-sided private information

We consider a rent-seeking contest where players compete in groups for a prize of given value. One group has private information about its number of members, which can be either small or large. The other groups have possibly different but publicly known sizes. We present an explicit characterization of the groups which are active in the unique equilibrium of the game, and relate the relative magnitude of group efforts to the size of the groups. We compare the decision of each type of the privately informed group to be active in equilibrium to the corresponding decision in a benchmark game with complete information.