Dynamic Pricing Under Consumer's Sequential Search

We study a firm offering a line of vertically differentiated perishable products with fixed initial inventory over a finite sales season. Consumers arrive at the firm randomly and inspect products sequentially until they find a product to purchase (if any). Consumers evaluate each product in terms of its overall utility revealed to them. Each consumer incurs a positive cost to inspect a product and hence may stop the sequential search without inspecting all the available items. Upon a product's inspection, the utility of the product is known to the consumer, who then decides whether to continue the search. We formulate the firm's and consumer's problems using stochastic dynamic programming and determine the consumers' optimal search decision, the firm's optimal price to charge for each product at each time and the optimal sequence in which to show the products to consumers. We show that consumers' optimal stopping rule, under certain conditions, is myopic and takes a threshold structure. We show that it is optimal for the firm to sequence products in decreasing order of product quality. We show that, in some cases, it is optimal for the firm to increase a perishable product's price over time. This result is in stark contrast to the common result from the literature that prices for perishable products should be reduced over time. However, the fact that a consumer may not be able to see all products during the search can cause the opposite price behavior