多项式logistic回归
同种类的
产品(数学)
计算机科学
集合(抽象数据类型)
计量经济学
数学优化
纳什均衡
经济
数学
机器学习
几何学
组合数学
程序设计语言
作者
Mahesh Gopalakrishnan,Heng Zhang,Zhiqi Zhang
摘要
Abstract 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.
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