Multicasting: A Game-Theoretic Method for Constructing an Efficient Multicast Tree

Abstract

In multicast routing, the path search process can be formulated as a network game where end-users are considered self-motivated players. Every end-user must pay a cost for the path to get the data from the source. Therefore, end-users want to construct the path from the source at the minimum possible cost. In order to get the minimum cost, end-users will keep modifying paths, which leads to instability. When no end-user can do better by modifying his path, the stable state is considered a Pure Nash equilibrium (PNE). The quality of PNE depends on the cost-sharing mechanism among the end-users of edges. Bringing PNE close to the social optimum (minimum total cost for all end-users) has always been a goal for various cost-sharing strategies. It constructs a cost-effective multicast tree for group communication. Many authors analyzed the cost-sharing mechanisms based on the Shapley value concept, far from the social optimum. Our study aims to identify a weighted cost-sharing mechanism and formulate the path construction process as a Multicast Tree Construction Game (MTCGame). This game employs an MTC algorithm to reach PNE. We prove that at least one PNE always exists in MTCGame. We analyze the quality of the PNE numerically.