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A note on a selfish bin packing problem

Author

Listed:
  • Ruixin Ma
  • György Dósa
  • Xin Han
  • Hing-Fung Ting
  • Deshi Ye
  • Yong Zhang

Abstract

In this paper, we consider a selfish bin packing problem, where each item is a selfish player and wants to minimize its cost. In our new model, if there are k items packed in the same bin, then each item pays a cost 1/k, where k ≥ 1. First we find a Nash Equilibrium (NE) in time O(n log n) within a social cost at most 1.69103OPT + 3, where OPT is the social cost of an optimal packing; where n is the number of items or players; then we give tight bounds for the worst NE on the social cost; finally we show that any feasible packing can be converged to a Nash Equilibrium in O(n 2 ) steps without increasing the social cost. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Ruixin Ma & György Dósa & Xin Han & Hing-Fung Ting & Deshi Ye & Yong Zhang, 2013. "A note on a selfish bin packing problem," Journal of Global Optimization, Springer, vol. 56(4), pages 1457-1462, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1457-1462
    DOI: 10.1007/s10898-012-9856-9
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    Citations

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    Cited by:

    1. György Dósa & Leah Epstein, 2019. "Quality of strong equilibria for selfish bin packing with uniform cost sharing," Journal of Scheduling, Springer, vol. 22(4), pages 473-485, August.
    2. Xin Chen & Qingqin Nong & Qizhi Fang, 2021. "An improved mechanism for selfish bin packing," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 636-656, October.
    3. Vittorio Bilò & Francesco Cellinese & Giovanna Melideo & Gianpiero Monaco, 2020. "Selfish colorful bin packing games," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 610-635, October.
    4. Dosa, Gyorgy & Kellerer, Hans & Tuza, Zsolt, 2019. "Using weight decision for decreasing the price of anarchy in selfish bin packing games," European Journal of Operational Research, Elsevier, vol. 278(1), pages 160-169.
    5. Q. Q. Nong & T. Sun & T. C. E. Cheng & Q. Z. Fang, 2018. "Bin packing game with a price of anarchy of $$\frac{3}{2}$$ 3 2," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 632-640, February.
    6. Chenhao Zhang & Guochuan Zhang, 0. "From packing rules to cost-sharing mechanisms," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    7. Xin Chen & Qingqin Nong & Qizhi Fang, 0. "An improved mechanism for selfish bin packing," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-21.
    8. György Dósa & Leah Epstein, 2019. "Pareto optimal equilibria for selfish bin packing with uniform cost sharing," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 827-847, April.
    9. Chenhao Zhang & Guochuan Zhang, 2022. "From packing rules to cost-sharing mechanisms," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1578-1593, October.
    10. Vittorio Bilò & Francesco Cellinese & Giovanna Melideo & Gianpiero Monaco, 0. "Selfish colorful bin packing games," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-26.

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