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. Ishow 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 benchmark 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.