Reward Design in Risk-Taking Contests

Following the risk-taking model of Seel and Strack, $n$ players decide when to stop privately observed Brownian motions with drift absorption at zero. They are then ranked according their level stopping paid a rank-dependent reward. We study problem principal who aims induce desirable equilibrium performance by choosing how much reward is attributed each rank. Specifically, we determine optimal schemes for principals interested in average given While former can be related inequality Lorenz sense, latter have surprising shape.