In this paper, we assume that the network resources are managed by several brokers, which are endowed with resources by a (remote) central resource manager according to several predetermined policies. Our focus is on autonomous multimedia users. We propose a novel resource management scheme, where resource brokers choose well-suited axiomatic bargaining solutions to divide their allocated resources among the users associated with them. These resource division solutions enable resource brokers to provide strict minimum video quality guarantees according to the (varying) number of multimedia users associated with them. Finally, we show that the proposed solution enables us to model the problem of selecting resource brokers by multimedia users as an unweighted congestion game, thereby ensuring convergence to a stationary distribution of users across resource brokers. We investigate the number of required users' switches to reach the stationary distribution, and quantify the fairness of the stationary distribution by introducing a novel quality fairness comparison metric for the users.