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Tighter price of anarchy for selfish task allocation on selfish machines

Author

Listed:
  • Xiayan Cheng

    (Hunan Normal University
    Hunan First Normal University)

  • Rongheng Li

    (Hunan Normal University)

  • Yunxia Zhou

    (Hunan Normal University)

Abstract

Given a set $$L = \{J_1,J_2,\ldots ,J_n\}$$ L = { J 1 , J 2 , … , J n } of n tasks and a set $$M = \{M_1,M_2, \ldots ,M_m\}$$ M = { M 1 , M 2 , … , M m } of m identical machines, in which tasks and machines are possessed by different selfish clients. Each selfish client of machine $$M_i \in M$$ M i ∈ M gets a profit equal to its load and each selfish client of task allocated to $$M_i$$ M i suffers from a cost equal to the load of $$M_i$$ M i . Our aim is to allocate the tasks on the m machines so as to minimize the maximum completion times of the tasks on each machine. A stable allocation is referred to as a dual equilibrium (DE). We firstly show that 4/3 is tight upper bound of the Price of Anarchy(PoA) with respect to dual equilibrium for $$m\in \{3,\ldots ,9\}$$ m ∈ { 3 , … , 9 } . And secondly $$(7m-6)/(5m-3)$$ ( 7 m - 6 ) / ( 5 m - 3 ) is an upper bound for $$m\ge 10$$ m ≥ 10 . The result is better than the existing bound of 7/5.

Suggested Citation

  • Xiayan Cheng & Rongheng Li & Yunxia Zhou, 2022. "Tighter price of anarchy for selfish task allocation on selfish machines," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1848-1879, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00556-6
    DOI: 10.1007/s10878-020-00556-6
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    References listed on IDEAS

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    1. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
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