Technical Note—Error Noted in “Robust Contract Designs: Linear Contracts and Moral Hazard” by Yu and Kong (2020)

One of the main results of Yu and Kong [Yu and Kong (2020) Robust contract designs: Linear contracts and moral hazard. Oper. Res. 68(5):1457–1473] is proposition 4, which states that the optimal robust contract with a piecewise linear concave agent utility only consists of progressive fixed payments and linear rewards with progressive commission rates. In this note, we present a proof-based counterexample to theoretically demonstrate the incorrectness of this result. We then perform a numerical analysis to illustrate that their proposed optimal contract can perform poorly. Finally, we identify the specific errors in their proofs that lead to this erroneous conclusion.

Supplemental Material: Codes are available at https://doi.org/10.1287/opre.2024.1221.