Sharing the Cost of Multicast Transmissions in Wireless Networks

A crucial issue in non-cooperative wireless networks is that of sharing the cost of multicast transmissions to different users residing at the stations of the network. Each station acts as a selfish agent that may misreport its utility (i.e., the maximum cost it is willing to incur to receive the service, in terms of power consumption) in order to maximize its individual welfare, defined as the difference between its true utility and its charged cost. A provider can discourage such deceptions by using a strategyproof cost sharing mechanism, that is a particular public algorithm that, by forcing the agents to truthfully reveal their utility, starting from the reported utilities, decides who gets the service (the receivers) and at what price. A mechanism is said budget balanced (BB) if the receivers pay exactly the (possibly minimum) cost of the transmission, and $eta$-approximate budget balanced ($eta$-BB) if the total cost charged to the receivers covers the overall cost and is at most $eta$ times the optimal one, while it is efficient if it maximizes the sum of the receivers’ utilities minus the total cost over all receivers’ sets. In this paper, we first investigate cost sharing strategyproof mechanisms for symmetric wireless networks, in which the powers necessary for exchanging messages between stations may be arbitrary and we provide mechanisms that are either efficient or BB when the power assignments are induced by a fixed universal spanning tree, or $(3ln(k +1))$-BB ($k$ is the number of receivers), otherwise. Then we consider the case in which the stations lay in a $d$-dimensional Euclidean space and the powers fall as $1/d^alpha$, and provide strategyproof mechanisms that are either 1-BB or efficient for $alpha=1$ or $d =1$. Finally, we show the existence of $2(3^d −1)$-BB strategyproof mechanisms in any $d$-dimensional space for every $alphageq d$. For the special case of $d=2$ such a result can be improved to achieve 12-BB mechanisms.