We consider competitive routing in multicast networks from a noncooperative game theoretical perspective. There are N users sharing a network, and each has to send a quantity of packets to a different set of addresses (each address must receive the same packets). To do this the user has only to send one copy of a packet, the network making the duplications of the packets at appropriate nodes (depending on the chosen trees). The routing choice of a user is how to split its flow between different multicast trees. We present different criteria for optimization of this type of game. We treat two specific networks and establish the uniqueness of the Nash equilibrium in these networks, as well as the uniqueness of link utilization at Nash equilibria for specific cost functions in networks with general topology. We also present a result for convergence to equilibria from an initial nonequilibrium state.
