Share the Multicast Payment Fairly

Multicast routing uses a structure, either a tree or a mesh, to connect the receivers to the source, thus saving the bandwidth. How to share the cost among the receivers in a certain fair way has been studied widely in literature. When the agents, either the links or the nodes, in the network are selfish, it is desirable to pay the agents in a proper way such that each agent still reveals its true cost, a property known as strategyproofness. Several strategyproof mechanisms have been proposed based on several different multicast structures, and it is natural that the payments instead of the costs should be shared among the receivers. Motivated by this, we study how the payment should be shared among the receivers in a fair way when the payment is computed via a strategyproof mechanism based on some low cost multicast structure. Specifically, when links are selfish agents, based on a strategyproof mechanism whose multicast tree is at most 2 times the optimal, we propose a payment sharing scheme that is 1 n2 -budget-balanced, cross-monotonic, and in the core. We also prove that there is no payment sharing scheme that can achieve β-budget-balance and cross-monotonicity for β = Ω( 1 n ). When both the relay agents and the receivers are selfish, we show a negative result: combining a strategyproof mechanism M for the relay agents and a fair sharing scheme ξ for the receivers does not necessarily imply a strategyproof mechanism overall.