Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Utilitarian resource assignment
Journal of Discrete Algorithms
Performance Guarantees of Local Search for Multiprocessor Scheduling
INFORMS Journal on Computing
The structure and complexity of Nash equilibria for a selfish routing game
Theoretical Computer Science
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
The price of anarchy on uniformly related machines revisited
Information and Computation
Computer Science Review
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In this paper, we revisit the inefficiency of Nash Equilibrium of scheduling games by considering the Price of Anarchy (PoA) as a function of r, which is the ratio between the maximum and minimum size of jobs. For the social costs of minimizing makespan and maximizing the minimum machine load of all machines, we obtain the PoA for two and three machines, and the bound is tight for any r=1. Lower bounds on the PoA for general number of machines are also presented.