Status classification by lottery contests

We study the optimal design of status classifications in organizational structures under the assumption that agents in a lottery (Tullock) contest care about their relative position. For each such a contest with any number of status categories that is smaller than or equal to the number of agents, we provide sufficient conditions for the optimal partition, which is the distribution of agents among the status categories that maximizes the agents’ symmetric equilibrium effort. We show that, for any number of status categories, in the optimal partition of status categories, the higher the status category, the more agents are included in it. However, in the optimal partition of status categories, a higher status category may not contain more agents than a lower status category when agents receive monetary rewards in addition to the payoff from their relative position (status).