Delegation with Incomplete and Renegotiable Contracts

It is well known that delegating the play of a game to an agent via incentive contracts may serve as a commitment device and hence provide a strategic advantage. Previous literature has shown that any Nash equilibrium outcome of an extensive-form principals-only game can be supported as a sequential equilibrium outcome of the induced delegation game when contracts are unobservable and non-renegotiable. In other words, in extensive-form games, contracts may affect the equilibrium outcome even when they are unobservable as long as they cannot be renegotiated. In this paper we analyze the equilibrium outcomes of delegation games with unobservable and renegotiable contracts under the assumption that the principal cannot observe every history in the game when played by her agent. This informational assumption implies that contracts are incomplete and we show that such incompleteness restricts the set of equilibrium outcomes to a subset of Nash equilibrium outcomes even without renegotiation. Introducing renegotiation, in general, imposes further constraints and in some games implies that only subgame perfect equilibrium outcomes of the original game can be supported. However, there is a large class of games in which non-subgame perfect equilibrium outcomes of the principals-only game can also be supported, and hence delegation still has a bite even under renegotiable contracts