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.

💡 Research Summary

The paper revisits two standard assumptions of classical contract theory—delegated contracts and perfect commitment—and asks whether they remain without loss of generality in a common‑agency setting, where multiple principals interact with a single agent. In the single‑principal case, any non‑delegated contract can be replicated by a delegated one without affecting incentive compatibility, but perfect commitment is known to be restrictive. The authors show that, when several principals are present, the combination of non‑delegated contracts and imperfect commitment fundamentally alters the set of equilibrium allocations.

First, they demonstrate that allowing non‑delegated contracts expands the equilibrium outcome set. By constructing two examples with public announcement, they exhibit Pareto‑efficient allocations that cannot be supported by any equilibrium with delegated contracts, yet can be sustained when contracts merely restrict the agent’s choice to a subset of actions (non‑delegated). The key mechanism is the “menu‑of‑menus” contract: each principal offers a collection of menus, and the agent selects one menu from each collection after observing all contracts and messages. This structure lets principals coordinate their choices on the designated menus, achieving allocations that are impossible under delegated contracts because of conflicting interests.

The classic menu theorem (Peters 2001; Martimort & Stole 2002), which states that it is without loss of generality to focus on menu contracts in common agency, holds only under delegated contracts and perfect commitment. The paper proves that the theorem fails as soon as either assumption is relaxed. To restore a tractable characterization, the authors introduce four canonical contract classes:

1. CP (Classic Menu Contracts) – the standard delegated menu contracts.
2. CR (Menu‑of‑Menu with Recommendation) – each principal offers multiple menus together with a recommendation message for each menu.
3. CF (Menu‑of‑Menu with Full Recommendation) – a restricted version of CR where recommendations are less flexible but still sufficient to implement off‑equilibrium deviations.
4. CF* – an extension of CF that includes certain degenerate contracts.

They consider four extreme protocol environments defined by the combination of announcement (public vs. private) and communication (public vs. private):

• Private announcement & private communication – non‑delegated contracts add nothing; equilibrium outcomes are the same as with delegated contracts (Theorem 4).
• Public announcement & private communication – equilibrium paths can be captured by CR, while off‑equilibrium paths require CF.
• Public announcement & public communication – same as the previous case: CR on‑path, CF off‑path.
• Private announcement & public communication – on‑path contracts are captured by CR, but off‑path implementation needs the richer class CF*.

These “generalized menu theorems” show precisely which contract class is sufficient for each protocol and for on‑ versus off‑equilibrium behavior. The analysis reveals an asymmetric requirement: the contract space needed to replicate equilibria on the equilibrium path can be much smaller than that needed to replicate all possible deviations off the path.

Finally, the authors link the non‑delegated‑contract model to the literature on imperfect commitment (Bester & Strausz 2001; Doval & Skreta 2021). They prove that common agency with non‑delegated contracts is a special case of common agency with imperfect commitment, establishing a rigorous relationship between the two frameworks. Consequently, the generalized menu theorems also serve as a counterpart to the revelation principle under imperfect commitment, extending the insight that transparent, recommendation‑based mechanisms can implement any incentive‑compatible allocation even when some payoff‑relevant factors are not fully contractible.

Overall, the paper makes three major contributions: (i) it shows that non‑delegated contracts enlarge the set of feasible equilibria in common‑agency games; (ii) it identifies the failure of the classic menu theorem and proposes four canonical contract families that together restore a loss‑less representation; (iii) it connects these results to the imperfect‑commitment literature, providing a unified theory of contract design for multi‑principal environments with either non‑delegation or limited commitment. The findings have direct implications for policy domains where contract transparency is mandated (e.g., lobbying disclosures, pharmaceutical pricing contracts), suggesting that such transparency can indeed affect equilibrium outcomes when multiple principals interact.