Incentive Design and Pricing Under Limited Inventory

Problem definition: A firm faces random demand for a service it delivers on a given future date. To boost demand, the firm hires a sales agent who exerts unobservable effort continuously over time. The firm is concerned not only with increasing current demand, but also with smoothing demand over time to avoid losing goodwill if realized demand exceeds available inventory. Methodology/results: We study the firm’s incentive design problem using a novel continuous-time principal-agent framework, in which demand drifts over time in response to the agent’s unobserved effort, as well as 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 parameter values calibrated from the airline industry, we numerically show that under dynamic pricing, the use of a static incentive scheme helps the firm reap nearly all the benefits of the corresponding dynamic incentive scheme. In contrast, the use of a fully static strategy results in a significant loss of efficiency. Managerial implications: Comparing partially dynamic strategies, we find that dynamic contracting outperforms dynamic pricing when inventory is abundant. However, under limited inventory, the relative advantage depends nonmonotonically on demand elasticity: dynamic pricing dominates over the empirically relevant range of moderate to high elasticity, whereas dynamic contracting becomes more effective when elasticity is very low or in theoretical limits of extreme elasticity.

History: This paper was selected as part of the 1RR initiative between the M&SOM journal and the MSOM Society. This paper was part of the 2024 MSOM Interface of Finance, Operations and Risk Management (iFORM) SIG Conference.

Funding: R. Zuo acknowledges funding support from the Guangzhou Municipal Education Bureau University Research Project [Grant 2024312314] and the Guangzhou-HKUST(GZ) Joint Funding Program [Grant 2024A03J0630]. T. Dai was partially supported by the Bernard T. Ferrari Professorship at Johns Hopkins University. J. Keppo acknowledges funding support from the National Research Foundation, Singapore, and A*STAR under its RIE2020 Industry Alignment Fund–Industry Collaboration Projects grant call [IAF-ICP Grant No. I2001E0059, SIA-NUS Digital Aviation Corp Lab].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2026.0118.