Dynamic Pricing and Inventory Management Under Network Externality

Abstract

We study the impact of network externalities upon a firm’s pricing and inventory policy under demand uncertainty. The firm sells a product associated with an online service or communication network, which is formed by (part of) the customers who have purchased the product. The product exhibits network externalities, i.e., a customer’s willingness-to-pay and, thus, the potential demand are increasing in the size of the associated network. We show that a network-size-dependent base-stock/list-price policy is optimal. Moreover, the inventory dynamics of the firm do not influence the optimal policy as long as the initial inventory is below the initial base-stock level. Hence, we can reduce the the dynamic program to characterize the optimal policy to one with a single-dimensional state-space (the network size). Network externalities give rise to the tradeoff between generating current profits and inducing future demands, thus having several important implications upon the firm’s operations decisions. Compared with the benchmark case without network externalities, the firm under network externalities sets a higher base-stock level, and charges a lower [higher] sales price when the network size is small [large]. When the market is stationary, the firm adopts the introductory price strategy, i.e., it charges a lower price at the beginning of the sales season to induce higher future demands. The price discrimination and network expanding promotion strategies can effectively leverage network externalities and improve the firm's profit. Both strategies facilitate the firm to (partially) separate generating current profits and inducing future demands through network externalities. Finally, we perform extensive numerical studies to demonstrate the significant profit loss of ignoring network externalities. We also propose near-optimal heuristic policies that leverage network externalities by balancing generating current profits and inducing demands in the near future.