Competition in Parallel-Serial Networks

We study the efficiency implications of competition among profit-maximizing service providers in communication networks. Service providers set prices for transmission of flows through their (sub)network. The central question is whether the presence of prices will help or hinder network performance. We investigate this question by considering the difference between users' willingness to pay and delay costs as the efficiency metric. Previous work has demonstrated that in networks consisting of parallel links, efficiency losses from competition are bounded. Nevertheless, parallel-link networks are special, and in most networks, traffic has to simultaneously traverse links (or subnetworks) operated by independent service providers. The simplest network topology allowing this feature is the parallel-serial structure, which we study in this paper. In contrast to existing results, we show that in the presence of serial links, the efficiency loss relative to the social optimum can be arbitrarily large. The reason for this degradation of performance is the double marginalization problem, whereby each serial provider charges high prices not taking into account the effect of this strategy on the profits of other providers along the same path. Nevertheless, when there are no delay costs without transmission (i.e., latencies at zero are equal to zero), irrespective of the number of serial and parallel providers, the efficiency of strong oligopoly equilibria can be bounded by 1/2, where strong oligopoly equilibria are equilibria in which each provider plays a strict best response and all of the traffic is transmitted. However, even with strong oligopoly equilibria, inefficiency can be arbitrarily large when the assumption of no delay costs without transmission is relaxed.