Contests between groups of unknown size

We consider group contests where the number of competing groups is fixed but group sizes are stochastic and unobservable to contest participants at the time of investment. We allow for arbitrary correlation between group sizes. When the distribution of group sizes is symmetric, the symmetric equilibrium aggregate investment is always lower than in a symmetric group contest where the same expected group size is commonly known. The same holds for asymmetric distributions of group sizes in contests between two groups. The reduction in investment due to population uncertainty is stronger the larger the variance in appropriately defined 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.