Energy Consumption in Radio Networks: Selfish Agents and Rewarding Mechanisms

We consider the range assignment problem in ad-hoc wireless networks in the context of selfish agents: a network manager aims in assigning transmission ranges to the stations so to achieve the strong connectivity of the network with a minimal overall energy; stations are not directly controlled by the manager and may refuse to transmit with a certain transmission range because this results in a power consumption proportional to that range. We investigate the existence of payment schemes which induce the stations to cooperate with a network manager computing a range assignment, that is, truthful mechanisms for the range assignment problem. We provide both positive and negative results on the existence of truthful VCG-based mechanisms for this NP-hard problem. We prove that (i) in general, e ery polynomial-time truthful VCG-based mechanism computes a solution of cost far-off the optimum, unless P=NP, and (ii) there exists a polynomialtime truthful VCG-based mechanism achieving a constant approximation for practically relevant, still NP-hard, versions, i.e. the metric and the well spread case.