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.
