Contract design and non-cooperative renegotiation

We study a contract design setting in which the contracting parties cannot commit not to renegotiate previous contract agreements. In particular, we characterize the outcome functions that are implementable for an uninformed principal and an informed agent if, having observed the agent's contract choice, the principal can offer a new menu of contracts in its place. An outcome function can be implemented in this setting if and only if it is optimal for the principal for some belief over agent types which is more pessimistic, in the sense of the likelihood ratio order, than the prior. Furthermore, the outcome function cannot be too sensitive to variations in the agent's type. We show that the direct revelation mechanism which implements such a function when renegotiation can be prevented will also implement it in any equilibrium when it cannot, so the standard contract is robust to renegotiation.