Competitive Routing in Multi-User Communication Networks
We consider a communication network shared by several selfish users. Each user seeks to optimize its own performance by controlling the routing of its given flow demand, giving rise to a non-cooperative game. We investigate the Nash equilibrium of such systems. For a two-node multiple-links system, uniqueness of the Nash equilibrium is proved under reasonable convexity conditions. It is shown that this Nash equilibrium point possesses interesting monotonicity properties. For general networks, these convexity conditions are not sufficient for guaranteeing uniqueness, and a counter example is presented. Nonetheless, uniqueness of the Nash equilibrium for general topologies is established under various assumptions. 1 1 Introduction Traditional computer networks were designed with a single administrative domain in mind. That is, the network is designed and operated as a single entity with a single control objective. A single control objective does not mean that control is central..