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The price of fairness for a two-agent scheduling game minimizing total completion time

Author

Listed:
  • Yubai Zhang

    (East China University of Science and Technology)

  • Zhao Zhang

    (Zhejiang Normal University)

  • Zhaohui Liu

    (East China University of Science and Technology)

Abstract

This paper studies the price of fairness in a two-agent single machine scheduling game. In this game, two agents compete to perform their jobs on a common single machine. Both of the two agents want to minimize their own total completion time. One of them has exactly two jobs. All processing times are positive. We show that all Kalai-Smorodinsky fair schedules can be found in linear time, and its price of fairness equals a half.

Suggested Citation

  • Yubai Zhang & Zhao Zhang & Zhaohui Liu, 0. "The price of fairness for a two-agent scheduling game minimizing total completion time," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-19.
  • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00581-5
    DOI: 10.1007/s10878-020-00581-5
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    References listed on IDEAS

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    1. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    2. Forsythe Robert & Horowitz Joel L. & Savin N. E. & Sefton Martin, 1994. "Fairness in Simple Bargaining Experiments," Games and Economic Behavior, Elsevier, vol. 6(3), pages 347-369, May.
    3. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
    4. Nicosia, Gaia & Pacifici, Andrea & Pferschy, Ulrich, 2017. "Price of Fairness for allocating a bounded resource," European Journal of Operational Research, Elsevier, vol. 257(3), pages 933-943.
    5. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    6. Wellman, Michael P. & Walsh, William E. & Wurman, Peter R. & MacKie-Mason, Jeffrey K., 2001. "Auction Protocols for Decentralized Scheduling," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 271-303, April.
    7. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
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