Abstract
This paper studies the inefficiency of Nash equilibria (NE) for scheduling games on hierarchical machines with quadratic social cost. There is a set of hierarchical machines and a set of jobs. Each job can choose one machine from the set of machines that are permitted to process it, and the cost associated with the job is equal to the load of the selected machine. A schedule is an NE if no job can reduce its cost by ultimately moving to a different eligible machine. The social cost is the sum of squares of the loads of all the machines. We show that the Price of Anarchy for two, three and four machines is [Formula: see text], [Formula: see text] and [Formula: see text], respectively.
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