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Moore interval subtraction and interval solutions for TU-games

Author

Listed:
  • S. Zeynep Alparslan Gök

    (Süleyman Demirel University)

  • René van den Brink

    (VU University Amsterdam)

  • Osman Palancı

    (Süleyman Demirel University)

Abstract

Standard solutions for cooperative transferable utility (TU-) games assign to every player in a TU-game a real number representing the player’s payoff. In this paper, we introduce interval solutions for TU-games which assign to every player in a game a payoff interval. Even when the worths of coalitions are known, it might be that the individual payoff of a player is not known. According to an interval solution, every player knows at least a lower- and upper bound for its individual payoff. Therefore, interval solutions are useful when there is uncertainty about the payoff allocation even when the worths that can be earned by coalitions are known. Specifically, we consider two interval generalizations of the famous Shapley value that are based on marginal contributions in terms of intervals. To determine these marginal interval contributions, we apply the subtraction operator of Moore. We provide axiomatizations for the class of totally positive TU-games. We also show how these axiomatizations can be used to extend any linear TU-game solution to an interval solution. Finally, we illustrate these interval solutions by applying them to sequencing games.

Suggested Citation

  • S. Zeynep Alparslan Gök & René van den Brink & Osman Palancı, 2024. "Moore interval subtraction and interval solutions for TU-games," Annals of Operations Research, Springer, vol. 343(1), pages 293-311, December.
    • Handle: RePEc:spr:annopr:v:343:y:2024:i:1:d:10.1007_s10479-024-06265-1
    DOI: 10.1007/s10479-024-06265-1
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    References listed on IDEAS

    as
    1. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
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    6. Alparslan Gök, S.Z. & Branzei, O. & Branzei, R. & Tijs, S., 2011. "Set-valued solution concepts using interval-type payoffs for interval games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 621-626.
    7. S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 99-109, March.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cooperative TU-game; Interval game; Moore subtraction; Moore-Shapley interval solution;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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