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Risk Aversion and Information in Robust Contracting

Primarily human-written textHuman understanding: all partsmath.OC — Optimization and Control

Contributed by Ruixue Yuan ↗, Zhenyu Sun ↗

Version 1 / Oct 26, 2026 / CC BY 4.0

Abstract

We study hidden-action contracting with a risk-averse agent and partial knowledge of actions in a compact convex envelope of distribution--cost pairs. With finitely many outcomes and bounded deterministic wages, the principal's worst-case payoff admits an exact dual representation with an endogenous ff-divergence governed by transfer utility and an incentive multiplier. Under strictly concave utility, finite-multiplier branch optima follow a truncated likelihood-ratio rule, including at zero-probability outcomes. To address nonattainment induced by adversarial tie-breaking, we characterize the infinite-multiplier limit as a restricted zero-sum game. For polyhedral envelopes, we establish two-sided O(1/λ)O(1/\lambda) convergence when inverse utility is Lipschitz. Positive tolerance for suboptimal agent responses restores existence and confines the multiplier search to an explicit compact interval. A finite optimal multiplier gives a linear upper bound on tolerance loss; an optimal infinite-multiplier endpoint in a polyhedral envelope gives a square-root upper bound. A two-action example attains the square-root rate asymptotically. Restricting contracts to a coarse performance statistic contracts the endogenous divergence. We characterize equality in data processing under wage bounds, bracket the value of finer contractible information using fine and coarse dual minimizers, and derive quantitative bounds for approximately sufficient statistics. Numerical experiments demonstrate strict gains over utility-affine contracts and distinguish technological knowledge from the richness of contractible performance signals.

Provenance statement

ChatGPT and Codex (OpenAI) were used for proofreading and language editing, numerical code development, and checking mathematical arguments and computational results. The authors take full responsibility for the mathematical arguments, computations, and final text. Numerical experiments use Python, NumPy, SciPy, and Matplotlib.

Tools used

OpenAI
ChatGPT

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Version history

  1. v1Submitted by Zhenyu SunInitial depositCurrentOct 26, 2026