The price of anarchy in competing differentiated services networks

We investigate competition between network providers that offer service to two types of traffic differing in their sensitivity to delay. We first consider competition amongst network providers who offer differentiated services by providing a priority queue for the delay sensitive traffic. We compare this to a situation in which all the competing network providers have network architectures that treat traffic of both types the same way. Our model of competition is Cournot in that service providers choose a rate to offer traffic of each type, and in-turn the total rate offered to each type of traffic determines the price of each traffic type. We are interested in the price of anarchy in these games of competition, which is defined as the ratio of the maximum achievable social utility versus the social utility attained when service providers selfishly maximize profits and reach a Nash equilibrium. We find that the price of anarchy is no more than 4/3 in our model of competing providers who offer differentiated services. In competition with providers that do not offer preferential service to delay sensitive traffic, we find the price of anarchy can be higher than 4/3, and we derive bounds for a number of important cases.