Dynamic pricing of differentiated products under competition with reference price effects using a neural network-based approach

Abstract

In this paper, we analyze the dynamic-pricing decisions of differentiated products for retailers operating in a competitive environment, for a finite-time horizon, limited initial inventory, and in the presence of the reference effect. Customers learn from the past prices of retailers and form their estimate of sales prices, called the reference price effect, and use it to make a decision on choosing a retailer to make a purchase. The demand is uncertain, and the customer choice behavior is modeled based on a Multinomial Logit model, modified to incorporate the reference effect. The complexity of the problem increases under conditions of competition and demand uncertainty and cannot be analyzed using conventional methods. Therefore, we have used a neural network-based algorithm called Revenue-Based Neural Network (RBNN) to dynamically calculate the competitive price in order to increase the retailer’s revenue. We have analyzed the effect of competition and the performance of RBNN algorithm under two scenarios: a monopolistic situation in which a retailer uses the RBNN policy to maximize its revenue, and a duopolistic situation in which one retailer uses the RBNN strategy and the other uses an adaptive policy called Derivative Following (DF). The results of the experiments show that the pricing policy under duopolistic conditions highly affects the income of retailers in the presence of reference price. The RBNN policy outperforms the DF policy due to the learning process on the customers’ reference price. By charging higher prices in the RBNN strategy, the seller trades off the current revenue with the long-term revenue resulting from formation of higher levels of the reference price in customers’ minds and earns more revenue than its competitor overall.