A firm faces random demand for a service it delivers on a given future date. To boost the demand, the firm hires a sales agent who exerts unobservable effort continuously over time. The firm is concerned not only about boosting current demand, but also about smoothing the demand over time to avoid the loss of goodwill when the realized demand exceeds its limited inventory. We model the firm’s incentive design problem using a continuous-time principal-agent framework in which demand drifts over time in response to unobserved agent effort and the price the firm charges. To induce the agent’s sales effort, the firm chooses an incentive scheme that depends on the remaining inventory and the time to the service (e.g., time to departure in the case of airlines). We characterize the firm’s optimal incentive scheme under both static and dynamic pricing policies. Using parameters calibrated from the airline industry, we numerically show that under dynamic pricing, a static incentive scheme provides nearly all of the benefit of the corresponding dynamic incentive scheme. By contrast, using a fully static strategy causes a substantial efficiency loss. We also compare two partially dynamic strategies under which the firm practices either dynamic pricing or dynamic contracting, but not both. Among other findings, we show that all else being equal, under a high inventory level, the dynamic-contracting-only strategy tends to outperform the dynamic-pricing-only strategy; under a tight inventory level, however, the dynamic-pricing-only strategy tends to perform better.
Professor Keppo teaches risk management and analytics courses, and directs analytics executive education programs at NUS Business School. He is also Research Director of the Institute of Operations Research and Analytics at NUS. Previously, he taught at the University of Michigan. He has several publications in the top-tier journals such as Journal of Economic Theory, Review of Economic Studies, Management Science, Operations Research, and Journal of Business on topics such as investment analysis, banking regulation, learning, and strategic incentives. His research has been featured also in numerous business and popular publications, including the Wall Street Journal and Fortune. Professor Keppo’s research has been supported by several Asian, European, and US agencies such as the National Science Foundation. He serves on the editorial boards of Management Science, Mathematics of Operations Research, and Journal of Risk. He has consulted several startups, Fortune 100 companies, and financial institutions.