Analysis of Price Competition in a Slotted Resource Allocation Game

Pricing telecommunication networks has become a highly regarded topic during the last decade, in order to cope with congestion by controlling demand, or to yield proper incentives for a fair sharing of resources. On the other hand, another important factor has to be brought in: there is a rise of competition between service providers in telecommunication networks such as for instance the Internet, and the impact of this competition has to be carefully analyzed. The present paper pertains to this recent stream of works. We consider a slotted resource allocation game with several providers, each of them having a fixed capacity during each time slot, and a fixed access price. Each provider serves its demand up to its capacity, demand in excess being dropped. Total user demand is therefore split among providers according to Wardrop's principle, depending on price and loss probability. Using the characterization of the resulting equilibrium, we prove, under mild conditions, the existence and uniqueness of a Nash equilibrium in the pricing game between providers. We also show that, remarkably, this equilibrium actually corresponds to the socially optimal situation obtained when both users and providers cooperate to maximize the sum of all utilities, this even if providers have the opportunity to artificially reduce their capacity.