Sharing the Cost of Multicast Transmissions in Wireless Networks

We investigate the problem of sharing the cost of a multicast transmission in a wireless network where each node (radio station) of the network corresponds to (a set of) user(s) potentially interested in receiving the transmission. As in the model considered by Feigenbaum et al [2001], users may act selfishly and report a false ”level of interest” in receiving the transmission trying to be charged less by the system. We consider the issue of designing a so called truthful mechanisms for the problem of maximizing the net worth (i.e., the overall ”happiness” of the users minus the cost of the transmission) for the case of wireless networks. Intuitively, truthful mechanism guarantee that no user has an incentive in reporting a false valuation of the transmission. Unlike the ”wired” network case, here the cost of a set of connections implementing a multicast tree is not the sum of the single edge costs, thus introducing a complicating factor in the problem. We provide both positive and negative results on the existence of optimal algorithms for the problem and their use to obtain VCG truthful mechanisms achieving the same performances.