Comment on “Optimal Contract to Induce Continued Effort” - Cao, Ping; Tian, Feng; Sun, Peng (Management Science, 2022)
In this comment, we first use a counterexample to demonstrate that the optimal contract structure proposed in section 4 of the paper [Sun P, Tian F (2018) Optimal contract to induce continued effort. Management Sci. 64(9):4193–4217] can be wrong when the two players’ discount rates are different. We then specify correct optimal contract structures, which involve generalizing the contract space to allow random termination. Numerical study with a wide range of model parameters illustrates that such a random termination only occurs sparingly in optimal contracts. Moreover, the suboptimality gap, measured by the relative improvement of the optimal contract over the best contract without random termination, is extremely small. This paper was accepted by Manel Baucells, decision analysis.