Pro t Maximizing Mechanisms for the Extended Multicasting Game

We consider the design of multicast networks when both edges and nodes are sel sh agents. Our objective is a budget-balanced, strategy-proof mechanism which selects the set of clients to receive service and extracts payments from those clients. It constructs a network to provide the service, pays edges to participate in the network, and aims to maximize pro t from the transaction. We introduce the notion of pro t guaranteeing mechanisms, and show the existence of one such mechanism. The mechanism provides guarantees of the form that in a suÆciently pro table market, it obtains some fraction of the obtainable pro t, and if the market is suÆciently unpro table, then the mechanism demonstrates that no pro table solution exists. The mechanism runs in polynomial time. To our knowledge, this is the rst study of mechanisms for designing multicast networks in which edge values are unknown.