Braess' phenomenon in the management of networks and dissociation of equilibrium concepts

Braess' phenomenon, also known as Braess' paradox, is a phenomenon that has received considerable attention in transportation engineering and planning, as well as in other fields. It has an important implication in the area of investment in transportation networks, namely that adding a new link in a network may increase the cost to the users of that network. In this paper we show this phenomenon in a new environment. Unlike traditional examples, which involve the physical addition of a link to a network (a 0/1 integer decision variable), an example is presented where the decision variable is continuous in nature. Moreover, this example conveys two new messages. First, it is shown that some logical criterion of assigning common resources among users of a network proportional to the number of users competing for common resources may not serve the purpose of efficiency in the sense of minimizing total user travel cost (time). Second, it is demonstrated that the very interdependence of variables and decisions may lead to multi-equilibrium solutions to the equilibrium flow problem, some of which may not satisfy the once taken for granted characteristic that if the flow pattern satisfies equilibrium conditions, then no user may be better off by unilaterally changing paths.