Complements and substitutes in common agency

Abstract In this paper we analyse the problem of the rent obtained by the agent in private common agency games. The key features for answering this question are the properties of the cost function of the agent. We prove that if this cost function is submodular (costs complements) then there is no equilibrium in which the agent makes a rent and if the cost function is supermodular (costs substitutes) then in all equilibria the agent makes a rent. We also examine the problem in some intermediate cases.