Dynamic Contract Design in the Presence of Double Moral Hazard
研究了无限时间范围内，委托人雇佣代理人提供服务时，因无法观察线下客户到达和代理人努力而引发的双重道德风险问题，并设计了包含支付方案和终止时间的简单最优合同。
We consider a stylized incentive management problem over an infinite time horizon, where the principal hires an agent to provide services to customers. Customers request service in one of two ways: either via an online or a traditional offline channel. The principal does not observe the offline customers’ arrivals, nor does she observe whether the agent exerts (costly) effort that can increase the arrival rate of customers. This creates an opportunity for the agent (i) to divert cash (that is, to under-report the number of offline customers and pocket respective revenues) and also (ii) to shirk (that is, not to exert effort), thus leading to a novel and thus far unexplored double moral hazard problem. To address this problem, we formulate a constrained, continuous-time, stochastic optimal control problem and derive an optimal contract with a simple intuitive structure that includes a payment scheme and a potential termination time of the agent. We enrich the model to allow the principal to either (i) dynamically adjust the prices for the services in both channels or (ii) monitor the agent. Both tools help the principal to alleviate the double moral hazard problem. We derive respective optimal strategies for using those tools that guarantee the highest profits. We show that the worse the agent’s past performance is, the lower the prices should be set and the more the principal should monitor the agent. This paper was accepted by Ilia Tsetlin, behavioral economics and decision analysis. Funding: The work of F. Tian is financially supported by the Hong Kong RGC Funding [RGC General Research Fund 2023/24 17502023], HKU Seed Fund for Basic Research for New Staff (2022), and the HKU Business School Shenzhen Research Institute [SZRI2023-BRF-04]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01169 .