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Bin packing game with a price of anarchy of $$\frac{3}{2}$$ 3 2

Author

Listed:
  • Q. Q. Nong

    (Ocean University of China)

  • T. Sun

    (Ocean University of China)

  • T. C. E. Cheng

    (The Hong Kong Polytechnic University)

  • Q. Z. Fang

    (Ocean University of China)

Abstract

We consider the bin packing problem in the non-cooperative game setting. In the game there are a set of items with sizes between 0 and 1 and a number of bins each with a capacity of 1. Each item seeks to be packed in one of the bins so as to minimize its cost (payoff). The social cost is the number of bins used in the packing. Existing research has focused on three bin packing games with selfish items, namely the Unit game, the Proportional game, and the General Weight game, each of which uses a unique payoff rule. In this paper we propose a new bin packing game in which the payoff of an item is a function of its own size and the size of the maximum item in the same bin. We find that the new payoff rule induces the items to reach a better Nash equilibrium. We show that the price of anarchy of the new bin packing game is $$\frac{3}{2}$$ 3 2 and prove that any feasible packing can converge to a Nash equilibrium in $$n^2-n$$ n 2 - n steps without increasing the social cost.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:2:d:10.1007_s10878-017-0201-6
    DOI: 10.1007/s10878-017-0201-6
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Chenhao Zhang & Guochuan Zhang, 0. "From packing rules to cost-sharing mechanisms," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    2. Xin Chen & Qingqin Nong & Qizhi Fang, 0. "An improved mechanism for selfish bin packing," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-21.
    3. 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.
    4. Chenhao Zhang & Guochuan Zhang, 2022. "From packing rules to cost-sharing mechanisms," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1578-1593, October.

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