Coordination mechanisms from (almost) all scheduling policies

We study the price of anarchy of coordination mechanisms for a scheduling problem where each job j has a weight wj, processing time pij, assignment cost hij, and communication delay (or release date) rij, on machine i. Each machine is free to declare its own scheduling policy. Each job is a selfish agent and selects a machine that minimizes its own disutility, which is equal to its weighted completion time plus its assignment cost. The goal is to minimize the total disutility incurred by all the jobs. Our model is general enough to capture scheduling jobs in a distributed environment with heterogeneous machines (or data centers) that are situated across different locations. Our main result is a characterization of scheduling policies that give a small (robust) Price of Anarchy. More precisely, we show that whenever each machine independently declares any scheduling policy that satisfies a certain bounded stretch condition introduced in this paper, the game induced between the jobs has a small Price of Anarchy. Our characterization is powerful enough to test almost all popular scheduling policies. On the technical side, to derive our results, we use a potential function whose derivative leads to an instantaneous smoothness condition, and linear programming and dual fitting. To the best of our knowledge, this is a novel application of these techniques in the context of coordination mechanisms, and we believe these tools will find more applications in analyzing PoA of games. We also extend our results to the lk-norms and l∞ norm (makespan) objectives.