Rent-seeking contests with private values and common knowledge about the mean

We study a rent-seeking contest in which players have heterogeneous and private valuations. In addition to their own type, agents only know that all valuations are drawn from a distribution, of which they only know the mean. We obtain a closed-form solution for agents' optimal level of investment and subject it to comparative statics analysis. We also investigate the issue of entry in the game and the amount of rent dissipation that results in equilibrium. Finally, we compare our results with those that would emerge in a context of perfect information.