Bounds on Benefits and Harms of Adding Connections to Noncooperative Networks

In computer networks (and, say, transportation networks), we can consider the situation where each user has its own routing decision so as to minimize noncooperatively the expected passage time of its packet/job given the routing decisions of other users. Intuitively, it is anticipated that adding connections to such a noncooperative network may bring benefits at least to some users. The Braess paradox is, however, the first example of paradoxical cases where it is not always the case. This paper studies the bounds on the degrees of coincident cost improvement (benefits) and degradation (harms) for all users by adding connections to noncooperative networks. For Wardrop networks (noncooperative networks with infinitesimal users), the degree of benefits for all users can increase without bound by adding connections whereas no Wardrop network has been found for which the degree of harms can increase without bound for all users. In contrast, for Nash networks (noncooperative networks with a finite number of users), the degrees of both benefits and harms can increase without bound for all users. On the other hand, we see that, for some category of Wardrop networks, adding connections to them can bring neither benefits nor harms to all users, and that, for some homogeneous networks, adding connections to them can never bring benefits to all users under any static policy including cooperative and noncooperative ones. Keywords— Braess paradox, Wardrop equilibrium, Nash equilibrium, coincident cost degradation and improvement, computer and communication networks, distributed computer systems, network routing, shortest path routing, source routing, static load balancing.