Punish Underperformance with Suspension: Optimal Dynamic Contracts in the Presence of Switching Cost

Abstract

This paper studies a dynamic principal–agent setting in which the principal needs to dynamically schedule an agent to work or be suspended. When the agent is directed to work and exert effort, the arrival rate of a Poisson process is increased, which increases the principal’s payoff. Suspension, on the other hand, serves as a threat to the agent by delaying future payments. A key feature of our setting is a switching cost whenever the suspension stops and the work starts again. We formulate the problem as an optimal control model with switching and fully characterize the optimal control policies/contract structures under different parameter settings. Our analysis shows that, when the switching cost is not too high, the optimal contract demonstrates a generalized control-band structure. The length of each suspension episode, on the other hand, is fixed. Overall, the optimal contract is easy to describe, compute, and implement. This paper was accepted by Ilia Tsetlin, behavioral economics and decision analysis. Funding: The work of P. Cao is financially supported by the National Natural Science Foundation of China [Grants 72122019 and 71771202]. The work of F. Tian is financially supported by the Hong Kong Research Grants Council (RGC) funding (RGC Early Career Scheme 2022/23) [Grant 27500822]. Supplemental Material: The e-companion and data are available at https://doi.org/10.1287/mnsc.2023.4845 .