Contests between groups of unknown size

We study group contests where group sizes are stochastic and unobservable to participants at the time of investment. When the joint distribution of group sizes is symmetric, with expected group size k¯, the symmetric equilibrium aggregate investment is lower than in a symmetric group contest with commonly known fixed group size k¯. A similar result holds for two groups with asymmetric distributions of sizes. For the symmetric case, the reduction in individual and aggregate investment due to group size uncertainty increases with the variance in relative group impacts. When group sizes are independent conditional on a common shock, a stochastic increase in the common shock mitigates the effect of group size uncertainty unless the common and idiosyncratic components of group size are strong complements. Finally, group size uncertainty undermines the robustness of the group size paradox otherwise present in the model.