High dimensional dynamic pricing with individual online review

¹ School of Accounting, Hunan University of Technology and Business, Changsha 410205, P.R. China
² Business School, Central South University, Changsha 410083, P.R. China
³ School of Accounting, Hunan University of Finance and Economics, Changsha 410205, P.R. China

^* Corresponding author: lisabarry@163.com

Received: 11 May 2024
Accepted: 27 June 2025

Abstract

This study explores how individual reviews affect a revenue maximizing monopolist’s optimal price from social learning perspective. We study this problem through three social learning model: a model based on summary measures of reviews, a model based on individual reviews and a model based on the combination of both. The dynamic pricing model built on the above three scenarios is a high-dimensional dynamic programming. To solve it effectively, we constructed an algorithm based on Smolyak grid points, which can change the grid points required in the value iteration process from exponential growth to polynomial growth. We demonstrate that it is more beneficial for the monopolist when customers read individual reviews after accounting for a product’s average rating. This benefit is particularly pronounced when a monopolist sells a niche product. However, if customers read only individual reviews and whether the monopolist can generate more revenue, depends on the customers’ initial beliefs.