Multiproduct pricing under the multinomial logit model with local network effects

作     者：Gopalakrishnan, Mohan Zhang, Heng Zhang, Zhiqi 

作者机构：Arizona State Univ WP Carey Sch Business Tempe AZ 85287 USA Washington Univ Olin Business Sch St Louis MO 63110 USA 

出 版 物：《DECISION SCIENCES》 (决策科学)

年 卷 期：2023年第54卷第4期

页      面：447-466页

核心收录：

学科分类：12[管理学] 120202[管理学-企业管理（含：财务管理、市场营销、人力资源管理）] 0202[经济学-应用经济学] 02[经济学] 1202[管理学-工商管理] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 

主　　题：convex optimization scoial network multinomial logit model multi-product pricing 

摘      要：Motivated by direct interactions with practitioners and real-world data, we study a monopoly firm selling multiple substitute products to customers characterized by their different social network degrees. Under the multinomial logit model framework, we assume that the utility a customer with a larger network degree derives from the seller s products is subject to more impact from her neighbors and describe the customers choice behavior by a Bayesian Nash game. We show that a unique equilibrium exists as long as these network effects are not too large. Furthermore, we study how the seller should optimally set the prices of the products in this setting. Under the homogeneous product-related parameter assumption, we show that if the seller optimally price-discriminates all customers based on their network degrees, the products markups are the same for each customer type. Building on this, we characterize the sufficient and necessary condition for the concavity of the pricing problem, and show that when the problem is not concave, we can convert it to a single-dimensional search and solve it efficiently. We provide several further insights about the structure of optimal prices, both theoretically and numerically. Furthermore, we show that we can simultaneously relax the multinomial logit model and homogeneous product-related parameter assumptions and allow customer in- and out-degrees to be arbitrarily distributed while maintaining most of our conclusions robust.