Dynamic Control of an Outsourcing Service System with Reentrant Customers

Abstract

Online marketplaces monetize seller access to demand through complex fee structures while managing strictly limited high-visibility capacity. We study how a retail platform should jointly choose a capacity-constrained featured assortment and per-unit selling fees when featured sellers compete on the platform. We formulate a Stackelberg game in which the platform selects the featured set and selling fees, and sellers then compete either in prices (Bertrand) or in market shares (Cournot) under multinomial logit demand. We characterize the platform’s optimal curation and fee policies and establish simple structural results. Our analysis shows that a decentralized platform should always fully utilize its display capacity, ranking sellers by an “adjusted-cost attractiveness” metric that balances demand potential with cost efficiency. Importantly, we demonstrate that Bertrand competition consistently generates higher platform revenue and market share than Cournot competition, driven by platform leadership in controlling product exposure and fee structures and the resulting intensified price competition among sellers. Finally, we study a cooperative pricing benchmark in which the platform coordinates retail prices while guaranteeing sellers target profit levels. This problem is NP-hard and may optimally leave display capacity unused when seller participation rents are high, in contrast to decentralized settings. These findings provide a theoretical foundation for jointly managing exposure and monetization in competitive digital marketplaces.