Combined competitive flow control and routing in networks with hard side constraints

We consider in this paper the problem of combined flow control and routing in a noncooperative setting, where each user is faced with a multi-criteria optimization problem, formulated as the minimization of one criterion subject to constraints on others. We address here the basic questions of existence and uniqueness of equilibrium. We show that an equilibrium indeed exists, but it may not be unique due to the multi-criteria nature of the problem. We are able, however, to obtain uniqueness in some weaker sense under appropriate conditions; we show in particular that the link utilizations are uniquely determined at equilibrium and the normalized Nash equilibrium is unique.