Free-riders in steiner tree cost-sharing games

Abstract. We consider cost-sharing mechanisms for the Steiner tree game. In this well-studied cooperative game, each selfish user expresses his/her willingness to pay for being connected to a source node s in an underlying graph. A mechanism decides which users will be connected and divides the cost of the corresponding (optimal) Steiner tree among these users (budget balance condition). Since users can form coalitions and misreport their willingness to pay, the mechanism must be group strategyproof: even coalitions of users cannot benefit from lying to the mechanism. We present new polynomial-time mechanisms which satisfy a standard set of axioms considered in the literature (i.e., budget balance, group strategyproofness, voluntary participation, consumer sovereignty, no positive transfer, cost optimality) and consider the free riders issue recently raised by Immorlica et al. [SODA 2005]: it would be desirable to avoid users that are connected for free. We also provide a number of negative results on the existence of polynomial-time mechanisms with certain guarantee on the number of free riders. Finally, we extend our technique and results to a variant considered by Biló et al. [SPAA 2004] with applications to wireless multicast cost sharing.