Hidden Commitment Power is Powerless

Abstract: A principal who offers a contract may renege when her default option is sufficiently attractive. The size of this temptation, which measures her commitment power, is often her private information. This paper asks how contracting outcomes change under this information asymmetry. Disciplining off-path beliefs with the Intuitive Criterion, I find that every type of principal behaves and earns payoffs exactly as if she were commonly known to have the least commitment power. Hidden commitment power is therefore powerless. The result delivers an unambiguous policy lesson on how to mitigate this information asymmetry prior to contracting: only measures that improve the worst case have value. Applied to credit rating, it rationalizes the monotone-partitional structure widely used in practice.

• The paper demonstrates that hidden commitment power yields no advantage, as all principals are forced into offering worst-case contracts.
• It employs a dynamic signaling model analyzed via Perfect Bayesian Equilibrium refined by the Intuitive Criterion to rule out separation.
• Numerical examples, such as debt issuance, reveal that equilibrium outcomes mirror those of the lowest-type principal regardless of private information.

Hidden Commitment Power in Contracting: A Technical Summary

Problem Setting and Motivation

The paper "Hidden Commitment Power is Powerless" (2606.02769) presents a formal analysis of principal-agent contracting under hidden information about commitment power. The central friction arises when a principal can renege on contractual promises if her default option is sufficiently attractive, i.e., contractual enforcement is imperfect. This temptation, the principal's "commitment power," is often privately known and not observable by the agent at the time of contracting.

The author situates the problem in canonical contexts—such as debt issuance and government procurement—where the principal's default option (collateral or legal penalties) directly influences the credibility of contractual offers and agent incentives. The central question is: How does hidden commitment power (private information about the size of the principal's temptation to default) alter equilibrium contracting outcomes?

Model Structure

The contracting game is framed as a dynamic signaling problem. The principal privately observes her commitment type, announces a contract, the agent updates beliefs, chooses an action, and the principal decides whether to honor the contract or default. The agent's incentives are weakened if he believes the principal may default. The game is analyzed using Perfect Bayesian Equilibrium (PBE) concepts, with further refinement via the Intuitive Criterion (Cho-Kreps).

Key assumptions encode:

• Strict monotonicity of the principal’s payoff in the agent’s action (she always prefers higher actions).
• Default payoffs are strictly decreasing in commitment power type (higher type = less temptation).
• A strict cost to providing stronger agent incentives (contracts that motivate the agent more strongly are more expensive to honor).

Main Results: Hidden Commitment Power is Powerless

The principal result is that hidden commitment power is completely powerless in disciplined equilibrium. Applying the Intuitive Criterion to refine off-path beliefs, all types of principals earn exactly the payoff—and must offer exactly the contract—that would prevail if everyone knew she had the weakest commitment power (largest temptation to default).

Formal statements:

• In every PBE surviving the Intuitive Criterion, each principal type earns the symmetric-information payoff of the lowest type, offering a contract the lowest type could honor.
• No separation occurs in equilibrium; contract offers are fully pooled and convey no information about the principal's type.
• Outcomes are invariant to the prior belief, and private commitment power confers no advantage.

This result is strongly contrasting with standard signaling models, where higher quality types can signal to separate and capture surplus. Here, even minimal refinement annihilates this possibility, collapsing all equilibrium variation to the worst-case pool.

Mechanism and Proof Intuition

Two mechanism components drive the result:

• Motive Separation: Honoring types value contract terms, but reneging types do not. In default-separation equilibrium candidates, honoring types benefit from tweaking contract terms; reneging types are indifferent.
• Partial Credibility: If a pooled contract is honored with intermediate probability (some types honor, some renege), a deviation that reduces contract cost can be uniquely attractive to honoring types if the agent updates belief to full commitment. This triggers off-path beliefs that support the deviation, violating equilibrium.

The Intuitive Criterion eliminates any equilibrium in which separation (default vs. honoring) is attempted, leaving only full pooling.

Numerical and Structural Highlights

The paper provides explicit analysis in a debt-issuance example, calibrating agent incentives and payoffs. Key results include:

• All equilibrium contracts offered are those sustainable by the lowest-type issuer (weakest commitment), regardless of the true collateral.
• Strong numerical monotonicity: issuer payoffs, interest rates, and agent investments are strictly increasing in commitment power under symmetric information but collapse to lowest-type values under hidden information and equilibrium refinement.

Implications for Information Design and Credit Rating

Policy implications are immediate. The only welfare-improving disclosure measures are those that raise the worst-case commitment power in posterior beliefs:

• Disclosure before contracting has value only if it excludes the weakest type from support. Signals that leave the lowest type in every posterior are welfare-equivalent to no disclosure.
• Optimal rating or classification systems are monotone-partitional: types are sorted into intervals, and terms are determined exclusively by the interval's lower threshold.
• Credit ratings (AAA, AA+, ...) are rationalized as optimal monotone partitions under complexity cost constraints.

Connections to Literature

The analysis intersects contracting with hidden commitment, signaling, and information design. Prior relational contracting literature (e.g., Halac, Lim, Kartik, Faingold, Lipnowski) selects equilibria favoring principals or Pareto outcomes; this paper demonstrates that signal game and refinement select the principal-least-preferred outcome instead, due to the signaling constraint imposed by hidden commitment power.

The result complements studies where slight friction or noise eliminates leader-follower advantages, here showing similar collapse in contracting payoff due to hidden commitment asymmetries.

Extensions and Discussion

The result persists (with minor technical modifications) under continuous types, rationalizable outside options, and (with stronger refinement) non-concave agent payoffs or settings with type-dependent default costs. The paper discusses institutional remedies such as public information, repeated interaction, or stronger enforcement devices—arguing these must break the baseline mechanism to enable better outcomes.

Conclusion

This paper delivers a rigorous analysis demonstrating that private information about commitment power eliminates any contracting benefit of higher types in refined equilibrium. Contract outcomes are indistinguishable from those generated by the weakest principal, and only policies addressing the worst-case type matter for welfare or information design. The technical framework and proof structure provide a robust foundation for further applications in principal-agent contracting, information design, and credit rating systems.