Are tournaments optimal over piece rates under limited liability for the principal?

Abstract

A highly acclaimed result is that tournaments are superior to piece rates when the agents are risk averse and their production activities are subject to a relatively large common shock. The reason is that tournaments allow the principal to trade insurance for lower income to the agents. Our analysis shows that this celebrated result does not carry over to the case when a limited liability (bankruptcy) constraint limits the payments the principal can make, provided that the liquidation value of the firm is sufficiently small. This finding has important implications for the vast number of limited liability firms. Even though limited liability becomes an issue for different ranges of liquidation values under the two schemes, tournaments are still superior when the liquidation value of the firm is intermediate or large, even though the limited liability constraint is still binding for intermediate values. Surprisingly, uncertainty in the price of output strengthens the need for tournaments by expanding the range of liquidation values over which tournaments are dominant, because price uncertainty introduces additional bankruptcy risk. These findings provide insight into policy implications in the contracting out of services by state and local governments, in procurement, in rent-seeking contests and in tournaments used by HMOs.