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Selfish bin coloring

Author

Listed:
  • Leah Epstein

    (University of Haifa)

  • Sven O. Krumke

    (University of Kaiserslautern)

  • Asaf Levin

    (The Technion)

  • Heike Sperber

    (University of Kaiserslautern)

Abstract

The bin packing problem, a classical problem in combinatorial optimization, has recently been studied from the viewpoint of algorithmic game theory. In this bin packing game each item is controlled by a selfish player minimizing its personal cost, which in this context is defined as the relative contribution of the size of the item to the total load in the bin. We introduce a related game, the so-called bin coloring game, in which players control colored items and each player aims at packing its item into a bin with as few different colors as possible. We establish existence of Nash and strong as well as weakly and strictly Pareto optimal equilibria in these games in the cases of capacitated and uncapacitated bins. For both kinds of games we determine the prices of anarchy and stability concerning those four equilibrium concepts. Furthermore, we show that extreme Nash equilibria, representatives of the set of Nash equilibria with minimal or maximal number of colors in a bin, can be found in time polynomial in the number of items for the uncapacitated case.

Suggested Citation

  • Leah Epstein & Sven O. Krumke & Asaf Levin & Heike Sperber, 2011. "Selfish bin coloring," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 531-548, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9302-1
    DOI: 10.1007/s10878-010-9302-1
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    References listed on IDEAS

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    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    2. Mingen Lin & Zhiyong Lin & Jinhui Xu, 2008. "Almost optimal solutions for bin coloring problems," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 16-27, July.
    3. Epstein, Amir & Feldman, Michal & Mansour, Yishay, 2009. "Efficient graph topologies in network routing games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 115-125, May.
    4. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    5. Andelman, Nir & Feldman, Michal & Mansour, Yishay, 2009. "Strong price of anarchy," Games and Economic Behavior, Elsevier, vol. 65(2), pages 289-317, March.
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    Cited by:

    1. Anna Angelucci & Vittorio Bilò & Michele Flammini & Luca Moscardelli, 2015. "On the sequential price of anarchy of isolation games," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 165-181, January.
    2. 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.
    3. 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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