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

One of the key claims in the paper “Robust Contract Designs: Linear Contracts and Moral Hazard” by Yu and Kong (2020) is proposition 4. This proposition states that when designing the best robust contract—assuming the agent’s utility function is piecewise linear and concave—the optimal solution involves only progressive fixed payments and linear rewards with progressive commission rates. In this note, we provide a clear counterexample backed by a detailed proof to show that this claim is actually incorrect. We further use numerical examples to demonstrate that the contract design suggested by Yu and Kong can perform significantly worse than expected. Lastly, we identify and explain the specific mistakes in their mathematical proofs that led them to this incorrect conclusion.