Common Shocks and Relative Compensation

This paper studies qualitative properties of an optimal contract in a multi-agent setting in which agents are subject to a common shock. We derive a necessary and sufficient condition for the optimal reward of an agent producing an output level y to be a decreasing (increasing) function of the outputs of the other agents, under the assumption that the agents’ outputs are informative signals of the value of the common shock. The condition is that the likelihood ratio p(y, e, η)/p(y, e′, η), where e is a higher effort level than e′ and η is the value of the common shock, be a decreasing (increasing) function of η. We give examples of applications of the result and examine its consequences for CEO compensation.