The Price of Anarchy in Two-Stage Scheduling Games

We consider a scheduling game, in which both the machines and the jobs are players. A job attempts to minimize its completion time by switching machines, while each machine would like to maximize its workload by choosing a scheduling policy from the given set of policies. We consider a two-stage game. In the first stage every machine simultaneously chooses a policy from some given set of policies, and in the second stage, every job simultaneously chooses a machine. In this work, we use the price of anarchy to measure the efficiency of such equilibria where each machine is allowed to use at most two policies. We provide nearly tight bounds for every combination of two deterministic scheduling policies with respect to two social objectives: minimizing the maximum job completion, and maximizing the minimum machine completion time.

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