Dynamic Pricing for Two-Sided Marketplaces with Offer Expiration

We consider a two-sided marketplace in which a market operator sells services to clients and buys services from vendors. The market operator determines the prices dynamically for both clients and vendors. Services are transacted in discrete units called jobs, and the jobs are characterized by their types, service deadlines, client prices, and vendor prices. Jobs are submitted by clients to the marketplace, and the market operator then lists the available jobs. Vendors can view the available jobs and choose them based on their preferences. We consider an infinite-horizon long-run average reward Markov decision process (MDP) model of the market operator’s dynamic pricing problem. The MDP consists of the arrival processes on both sides of the marketplace as well as the choice behavior of both clients and vendors. Because solving this MDP directly is impractical for large market sizes, we study a discrete-time fluid approximation of the problem. This approximation results in a simple pricing policy in which each job’s price trajectory depends on the time remaining until the service deadline but does not depend on the other jobs available in the marketplace. We show that this policy is asymptotically optimal with a loss ratio of order [Formula: see text] on the long-run average reward, where [Formula: see text] represents the scale of demand and supply. The performance of the fixed price trajectory policy is compared with other heuristics, including a constant pricing policy and a state-dependent pricing policy. We also extend the model to continuous-time and finite-horizon settings. This paper was accepted by Omar Besbes, revenue management and market analytics. Funding: The work of Y. Cao was partly supported by the National Natural Science Foundation of China [Grant 72201165, 72221001, 72231003, 72331006], and Shanghai Pujiang Program [Grant 22PJC066]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.00832 .