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Inefficiency of equilibria for the machine covering game on uniform machines

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Abstract

This paper studies a scheduling game on uniform machines with social cost of maximizing the minimum machine load. For the game with two machines, we present the (Strong) Price of Stability and (Strong) Price of Anarchy as a function of s, the ratio of the speeds of the two machines. These bounds are all tight for any value of s, thus the problem of measuring the inefficiency of equilibria on two uniform machines is completely solved. We also give the tight Price of Anarchy for a special case of three machines. From the results above, we achieve some new and interesting insights of scheduling games.

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Authors and Affiliations

  1. Department of Mathematics, State Key Lab of CAD and CG, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Zhiyi Tan

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Long Wan, Qi Zhang & Wei Ren

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  1. Zhiyi Tan
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  2. Long Wan
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  3. Qi Zhang
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  4. Wei Ren
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Correspondence to Zhiyi Tan.

Additional information

Supported by the National Natural Science Foundation of China (10971191, 60021201), Zhejiang Provincial Natural Science Foundation of China (LR12A01001) and Fundamental Research Funds for the Central Universities.

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Tan, Z., Wan, L., Zhang, Q. et al. Inefficiency of equilibria for the machine covering game on uniform machines. Acta Informatica 49, 361–379 (2012). https://doi.org/10.1007/s00236-012-0163-1

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  • DOI: https://doi.org/10.1007/s00236-012-0163-1

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