Common Agency with Non-Delegation or Imperfect Commitment

In classical contract theory, we usually impose two assumptions: delegated contracts and perfect commitment. While the second assumption is demanding, the first one suffers no loss of generality. Following this tradition, current common-agency models impose delegated contracts and perfect commitment. We first show that non-delegated contracts expand the set of equilibrium outcomes under common agency. Furthermore, the powerful menu theorem for common agency (Peters (2001) and Martimort and Stole (2002)}) fails for either non-delegated contracts or imperfect commitment. We identify canonical contracts in such environments, and re-establish generalized menu theorems. Given imperfect commitment, our results for common-agency models are analogous to those in Bester and Strausz (2001) and Doval and Skreta (2012) for the classical contract theory, which re-establish the revelation principle.