Competitive Routing in Multicast Communications

We consider competitive routing in multicast networks from a non-cooperative game theoretical perspective. N users share a network, each has to send an amount of packets to a different set of addressees (each address must receive the same packets), to do this it 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 of optimization for this type of games. We treat two specific networks, establish the uniqueness of the Nash equilibrium in several networks, as well as the uniqueness of links' utilization at Nash equilibria for specific cost functions in networks with general topology