Min-cost Selfish Multicast with Network Coding

The single-source min-cost multicast problem is considered, which can be framed as a convex optimization problem with the use of network codes and convex increasing edge costs. A decentralized approach to this problemn is presented by Lun, Ratnakar, et.al. for the case where all users cooperate to reach the global minimum. This paper analyzes the cost for the scenario where each of the multicast receivers greedily routes its flows and shows that a Nash equilibrium exists for such a scenario. An allocation rule by which the edge-cost at each edge is allocated to flows through that edge is presented. Under this rule, it is shown that for any (monomial) power-law cost function on each edge, there is a pricing rule such that the flow cost at user equilibrium is the same as the min-cost. This leads to the construction of an autonomous flow-steering algorithm for each receiver, which is also globally optimal. The algorithm is extended for completely distributed flow adaptation at nodes in the network, which also achieves globally minimal cost in steady state. Finally, the framework is generalized to the case of multiple multicast sessions and the results are shown to hold for user equilibrium in this case as well.