Selfish Scheduling with Setup Times

We study multiprocessor scheduling games with setup times on identical machines. Given a set of scheduling policies (coordination mechanism) on the machines, each out of $n$ players chooses a machine to assign his owned job to, so as to minimize his individual completion time. Each job has a processing length and is of a certain type. Same-type jobs incur a setup overhead to the machine they are assigned to. We study the Price of Anarchy with respect to the makespan of stable assignments, that are pure Nash or strong equilibria for the underlying strategic game. We study in detail the performance of a well established preemptive scheduling mechanism. In an effort to improve over its performance, we introduce a class of mechanisms with certain properties, for which we examine existence of pure Nash and strong equilibria. We identify their performance limitations, and analyze an optimum mechanism out of this class. Finally, we point out several interesting open problems.