Scheduling without Payments

Abstract

We consider mechanisms without payments for the problem of scheduling unrelated machines. Specifically, we consider truthful in expectation randomized mechanisms under the assumption that a machine (player) is bound by its reports: when a machine lies and reports value $\tilde{t}_{ij}$ for a task instead of the actual one t _ij , it will execute for time $\tilde{t}_{ij}$ if it gets the task—unless the declared value $\tilde{t}_{ij}$ is less than the actual value t _ij , in which case, it will execute for time t _ij . Our main technical result is an optimal mechanism for one task and n players which has approximation ratio (n + 1)/2. We also provide a matching lower bound, showing that no other truthful mechanism can achieve a better approximation ratio. This immediately gives an approximation ratio of (n + 1)/2 and n(n + 1)/2 for social cost and makespan minimization, respectively, for any number of tasks.