Dynamic network-based discriminatory pricing

We study the dynamic pricing decisions for competitive network service providers. We assume that each competing firm follows a three-part pricing scheme, which consists of an ongoing membership fee, a usage fee for communications within the networks, and another usage fee for communications across the networks. The difference between the two usage fees is the network-based price discount that allows price discrimination. We study the firms problems as a differential game and establish the optimal pricing policy as a Nash equilibrium feedback strategy depending on only the network sizes (i.e., the number of subscribers). We compare the dynamic network-based discount with the static discount. In the special case of a uniform calling pattern, we find that the firm network-based dynamic discount is always lower than the static discount; we find also that the firm that has a larger network can offer a bigger discount. These results are useful particularly for managers. To get further insights into the dynamic pricing policies, we explore the case of symmetric competition using numerical simulation.