Distributional Robustness of Linear Contracts

A new paper from Shiliang Zuo, published on arXiv (2604.24732), provides a rigorous mathematical justification for why linear contracts dominate in real-world principal-agent problems. The study addresses a key gap: while optimal contract theory often prescribes complex nonlinear structures, linear contracts are ubiquitous in practice. Zuo shows that when the principal faces distributional ambiguity—knowing only the expected signal for each effort level, not the full distribution—linear contracts are optimal for maximizing worst-case payoff. The proof introduces a novel concavification approach centered on self-inducing actions, where an affine contract simultaneously induces the action as optimal and supports the concave envelope of payments from above.

The results extend significantly to multi-party settings. In common agency with multiple principals, affine contracts improve all principals' worst-case payoffs. In team production with multiple agents, Zuo establishes a complementary necessity result: if any agent's contract is non-affine, the unique ex-post robust equilibrium is zero effort. The paper also shows that homogeneous utility and cost functions yield tractable characterizations, enabling closed-form approximation ratios and a sharp boundary between computational tractability. This work has immediate implications for contract design in AI alignment, supply chain management, and decentralized autonomous organizations, where robust, simple contracts are essential.