DP12887 It's not always best to be first
We study a model with n agents, each of whom has both a linear reward function that increases in the agent's effort and an effort constraint. However, since the effort (output) of the players has a negative effect on society the designer imposes a punishment such that the agent with the highest effort who caused the greatest damage is punished. We analyze the equilibrium of this model with either symmetric or asymmetric agents. At all the equilibrium points, all the agents are active and all have positive expected payoffs. We characterize the properties of the agents' equilibrium strategies and compare them to the well-known equilibrium strategies of the all-pay auction in which the agent with the highest effort wins a prize.