Allocation rules of indivisible prizes in team contests

We analyze contests in which teams compete to win indivisible homogeneous prizes. Teams are composed of members who may differ in their ability, and who exert effort to increase the success of their team. Each team member can obtain at most one prize as a reward. As effort is costly, teams use the allocation of prizes to give incentives and solve the free-riding problem. We develop a two-stage game. First, teams select a prize-allocation rule. Then, team members exert effort. Members take into account how their effort and the allocation rule influence the chance they receive a prize. We prove the existence and uniqueness of equilibrium. We characterize the optimal prize-assignment rule and individual and aggregate efforts. We then show that the optimal assignment rule is generally not monotonic.