Group-strategyproof cost sharing mechanisms for makespan and other scheduling problems

Classical results in economics show that no truthful mechanism can achieve budget balance and efficiency simultaneously. Roughgarden and Sundararajan recently proposed an alternative efficiency measure, which was subsequently used to exhibit that many previously known cost sharing mechanisms approximate both budget balance and efficiency. In this work, we investigate cost sharing mechanisms for combinatorial optimization problems using this novel efficiency measure, with a particular focus on scheduling problems. Our contribution is threefold: First, for a large class of optimization problems that satisfy a certain cost-stability property, we prove that no budget balanced Moulin mechanism can approximate efficiency better than Ω(logn), where n denotes the number of players in the universe. Second, we present a group-strategyproof cost sharing mechanism for the minimum makespan scheduling problem that is tight with respect to budget balance and efficiency. Finally, we show a general lower bound on the budget balance factor for cost sharing methods, which can be used to prove a lower bound of Ω(n) on the budget balance factor for completion and flow time scheduling objectives.