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Price of Anarchy of Scheduling Games on Hierarchical Machines with Quadratic Social Cost

Author

Listed:
  • Ling Lin

    (School of Computer & Computing Science, Hangzhou City University, Hangzhou 310015, P. R. China)

  • Zhiyi Tan

    (School of Mathematical Science, Zhejiang University, Hangzhou 310058, P. R. China)

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 3+5 4, 2+2 2 and 2+2 2, respectively.

Suggested Citation

  • Ling Lin & Zhiyi Tan, 2025. "Price of Anarchy of Scheduling Games on Hierarchical Machines with Quadratic Social Cost," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 42(02), pages 1-29, April.
    • Handle: RePEc:wsi:apjorx:v:42:y:2025:i:02:n:s0217595924500106
    DOI: 10.1142/S0217595924500106
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