The nature of tournaments

This paper characterizes the optimal way for a principal to structure a rank-order tournament in a moral hazard setting (as in Lazear and Rosen (1981)). We find that it is generally optimal to give rewards to top performers that are smaller in magnitude than corresponding punishments to poor performers. The paper identifies four reasons why the principal might prefer to give larger rewards than punishments: (i) R is small relative to P (where R is risk aversion and P is absolute prudence); (ii) the distribution of shocks to ouput is asymmetric and the asymmetry takes a particular form; (iii) the principal faces a limited liability constraint; and (iv) there is agent heterogeneity of a particular form. An intuition is given as to why these factors affect the optimal prize schedule. Using the theory developed by Green and Stokey (1983), we relate the results about tournaments to the structure of the optimal individual contract. The optimal individual contract typically punishes low output more than it rewards high output. We also give conditions under which the optimal individual contract will be a concave function of output.