New efficiency results for makespan cost sharing

In the context of scheduling, we study social cost efficiency for a cost-sharing problem in which the service provider's cost is determined by the makespan of the served agents' jobs. For identical machines, we give surprisingly simple cross-monotonic cost-sharing methods that achieve the essentially best efficiency Moulin mechanisms can guarantee. Still, our methods match the budget-balance of previous (yet rather intricate) results. Subsequently, we give a generalization for arbitrary jobs.Finally, we return to identical jobs in order to perform a fine-grained analysis. We show that the universal worst-case efficiency bounds from [T. Roughgarden, M. Sundararajan, New trade-offs in cost-sharing mechanisms, in: Proceedings of the 38th ACM Symposium on Theory of Computing, 2006] are overly pessimistic.