Large Tullock contests

We characterize the equilibrium effort function of a large Tullock contest game with heterogeneous agents under mild conditions on the contest success function and effort cost function. Later, writing the equilibrium total effort explicitly under a uniform type distribution, we identify the effort-maximizing large Tullock contest. It is shown that the contest designer needs to increase the curvature of the effective effort function, thereby encouraging high-type agents to exert even higher efforts, as the curvature of the effort cost function increases or the support of the type distribution gets narrower.