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The allowable value for cooperative games with restricted permutations

Author

Listed:
  • Xianghui Li

    (Henan University of Technology)

  • Bin Jiang

    (Jiaxing Nanhu University)

  • Yang Li

    (Henan University of Technology)

Abstract

This paper introduces a new framework for cooperative games with restricted permutations, focusing on situations where not all possible player permutations occur. The framework allows players within an ordered coalition to exchange positions if it benefits them. To ensure stable connections among players, we introduce the concept of stably connected ordered coalitions, which incorporates the notions of objection and counter-objection. We then define an order-restricted game, a generalized characteristic function game derived from the original game. Additionally, inspired by the Shapley value, we propose an allowable value and provide its axiomatization. Finally, we explore several extensions of this value to further investigate its potential applications.

Suggested Citation

  • Xianghui Li & Bin Jiang & Yang Li, 2024. "The allowable value for cooperative games with restricted permutations," Annals of Operations Research, Springer, vol. 340(2), pages 943-959, September.
  • Handle: RePEc:spr:annopr:v:340:y:2024:i:2:d:10.1007_s10479-024-06081-7
    DOI: 10.1007/s10479-024-06081-7
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    References listed on IDEAS

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    1. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-268.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. E. Algaba & J. M. Bilbao & J. J. López, 2004. "The position value in communication structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 465-477, July.
    4. Encarnación Algaba & René Brink & Chris Dietz, 2017. "Power Measures and Solutions for Games Under Precedence Constraints," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 1008-1022, March.
    5. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
    6. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
    7. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 221-236, November.
    8. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    9. Erfang Shan & Guang Zhang & Xiaokang Shan, 2018. "The degree value for games with communication structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 857-871, September.
    10. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
    11. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
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