601 / 2024-04-26 16:41:37

The Pricing Problem for Live-Streaming Commerce with Endogenous Market Size

revenue management,pricing optimization,FPTAS,MMNL,endogeneity

Live-streaming commerce, an emerging immersive business model, thrives on the real-time interaction between celebrities and consumers. This paper sheds light on a pivotal trade-off inherent in live-streaming commerce: the size of the followers' group is endogenous to the pricing strategy. To capture this endogeneity, we integrate the mixed multinomial logit (MMNL) model with a Markov Chain to depict the evolution of a celebrity's followers under any given pricing strategies. Additionally, this paper delineates two distinctions between followers and non-followers: their valuations in the MMNL model and their probabilities of attending each live-streaming show. When the two groups solely differ in arrival probabilities, we can derive the closed-form optimal pricing strategy and offer managerial insights into the circumstances under which live-streaming commerce surpasses traditional retailing. However, if the differences extend beyond arrival probabilities, the corresponding pricing problem becomes NP-hard. In such cases, we devise an FPTAS algorithm to identify an ϵ-optimal solution within polynomial time. Numerical experiments underscore the significance of considering the endogenous size of followers.