Inefficiency in provisioning interconnected communication networks

We model the Internet as a collection of Internet Service Providers (ISPs) that transit and peer to meet an exogenous demand for the transport of IP traffic among an arbitrary set of cities. The prices of bandwidth and of transit are also exogenous. ISPs are assumed to behave rationally and selfishly and therefore they provision the network that maximizes their own profit regardless of how expensive the overall network becomes. We call optimal to a network that ISPs would build if they cooperated to reduce overall provisioning costs; and we call inefficiency cost the additional cost to provision a network at Nash equilibrium relative to the provisioning cost of an optimal network. We show that inefficiency cost is primarily related to transit agreements. In fact, in a world where only peering agreements exist there is no inefficiency cost. However, networks with only peering agreements forgo the efficiencies of traffic aggregation. Transit agreements help reduce provisioning costs by realizing benefits from economies of scale. We show, by example, that there exist Nash networks that are strictly more expensive than optimal networks even when ISPs choose transit prices and therefore the market to provision communication networks with interconnection agreements designed they way the are today is inefficient. We show that inefficiency cost may be reduced, for example, by enforcing side payments between ISPs. We conclude with an analysis of the difficulties a regulator would face in endeavoring to move a market from am inefficient Nash equilibrium to optimality.