Group contests of incomplete information

We prove the existence of monotone pure strategy Bayesian equilibria in two types of contests between groups under incomplete information: (i) individual-level private information group contests, where each player only knows her own ability, and (ii) group-level private information group contests, where each player knows the abilities of all members of her group. In the latter case, we also show that the equilibrium is unique. We provide the results of exploratory numerical computations and discuss the qualitative properties of the equilibria.