Competitive routing in multi-user communication networks

A communication network shared by several selfish users is considered. Each user seeks to optimize its own performance by controlling the routing of its given flow demand, giving rise to a noncooperative game. The Nash equilibrium of such systems is investigated. For a two-node multiple-link system, the 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, the uniqueness of the Nash equilibrium is established under various assumptions