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

• 成果类型: Article
• 署名作者: Cao, Ping; Sun, Peng; Tian, Feng
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Duke University; University of Hong Kong
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.4845
• 发表日期: 2024
• 关键词: Dynamic contract; jump process; optimal control; switching cost

摘要

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.