Tournament Rewards and Risk Taking

I consider two seemingly unrelated puzzles; 1.Why is relative performance evaluation (RPE) used less in CEO compensation than agency theory suggests? 2.Why is sometimes, e.g., for fund managers, a mediocre performance more highly rewarded than excellence? I consider a simple tournament model, where agents can influence the spread of output in addition to its mean. I show that standard tournament rewards induce risky and lazy behavior from the agents. This finding sheds light on Puzzle 1. Second, I consider a scheme that ranks agents according to their relative closeness to a benchmar k. I show that there exists intermediate values of k such that the risky-lazy problem of the standard tournament can be mitigated. This result sheds light on Puzzle 2.