On the Convergence of Multicast Games in Directed Networks

We investigate the convergence of the price of anarchy after a limited number of moves in the classical multicast communication game when the underlying communication networks is directed. Namely, a subset of nodes of the network are interested in receiving the transmission from a given source node and can share the cost of the used links according to fixed cost sharing methods. At each step, a single receiver is allowed to modify its communication strategy, that is to select a communication path from the source, and assuming a selfish or rational behavior, it will make a best response move, that is it will select a solution yielding the minimum possible payment or shared cost. We determine lower and upper bounds on the price of anarchy, that is the highest possible ratio among the overall cost of the links used by the receivers and the minimum possible cost realizing the required communications, after a limited number of moves under the fundamental Shapley cost sharing method. In par...

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Angelo Fanelli, Michele Flammini, Luca Moscardelli
• Keywords: ALGORITHMICA 2010, Communication, Cost Sharing, Limited Number