Dynamic Pricing with Online Reviews

This paper investigates how the pricing policy of a revenue-maximizing monopolist is influenced by the social learning dynamics of customers who use online reviews to estimate the quality of the product. A salient feature of our problem is that the customers' willingness to pay, and hence the demand function, evolves over time in conjunction with the online reviews. The monopolist strives to maximize its total expected revenue over a finite horizon by adjusting prices in response to these dynamics. The revenue maximization problem is studied using two different review models: a quality-based review model, where customers report their experienced quality, and a value-based review model, where reviews internalize experienced quality as well as the purchase price. To formulate the problem in tractable form, we derive a fluid model that provides a good approximation of the system dynamics when the volume of sales is large. This formulation lends itself to key structural insights into the interactions between optimal pricing policies and review dynamics. In particular, we identify critical time scales and social learning regimes that sharply separate the efficacy of dynamic pricing vis-a-vis fixed-price strategies. Furthermore, we demonstrate the impact of the quality-based and value-based review models on key structural properties of the optimal pricing policies. These structural insights are also elucidated in an illustrative simulation study based on data from an online marketplace.