Optimal Large Population Tullock Contests

We consider large population Tullock contests in which agents are divided into different types according to their strategy cost function. A planner assigns type specific bias parameters to affect the likelihood of success with the objective of maximizing the Nash equilibrium level of aggregate strategy. We characterize such optimal bias parameters and identify conditions under which those parameters are increasing or decreasing according to the cost parameters. The parameters are biased in favor of high cost agents if the cost functions are strictly convex and the likelihood of success is sufficiently responsive to strategy. We also identify conditions under which a planner can truthfully implement the optimal parameters under incomplete information. In fact, under such conditions, dominant strategy implementation is equivalent to Nash implementation in our model. Hence, our mechanism double implements the optimal bias parameters.