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Consistency of the Owen value for TU-games with coalition and graph structures

Author

Listed:
  • Wenrong Lyu

    (Shanghai University)

  • Erfang Shan

    (Shanghai University)

  • Zeguang Cui

    (Shanghai University)

Abstract

Consistency is widely adopted in designing allocation rules for cooperative games. It imposes that the allocation rules give players the same payoff in the reduced game as in the initial cooperative game. The reduced game is obtained from the initial cooperative game by removing one or more players. In this paper, by extending the concept of consistency to cooperative games with coalition and graph structures, we establish a new axiomatization of the Owen graph value. Moreover, we give a comparison between the axiomatizations of the Owen, Banzhaf–Owen and symmetric coalitional Banzhaf graph values.

Suggested Citation

  • Wenrong Lyu & Erfang Shan & Zeguang Cui, 2024. "Consistency of the Owen value for TU-games with coalition and graph structures," Annals of Operations Research, Springer, vol. 338(2), pages 991-1017, July.
    • Handle: RePEc:spr:annopr:v:338:y:2024:i:2:d:10.1007_s10479-024-06073-7
    DOI: 10.1007/s10479-024-06073-7
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    References listed on IDEAS

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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. José Alonso-Meijide & M. Fiestras-Janeiro, 2002. "Modification of the Banzhaf Value for Games with a Coalition Structure," Annals of Operations Research, Springer, vol. 109(1), pages 213-227, January.
    4. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
    5. Anna Khmelnitskaya & Elena Yanovskaya, 2007. "Owen coalitional value without additivity axiom," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 255-261, October.
    6. Winter, Eyal, 1992. "The consistency and potential for values of games with coalition structure," Games and Economic Behavior, Elsevier, vol. 4(1), pages 132-144, January.
    7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    8. Bezalel Peleg, 1989. "An Axiomatization of the Core of Market Games," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 448-456, August.
    9. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    10. Alonso-Meijide, J.M. & Álvarez-Mozos, M. & Fiestras-Janeiro, M.G., 2009. "Values of games with graph restricted communication and a priori unions," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 202-213, September.
    11. Vazquez-Brage, Margarita & Garcia-Jurado, Ignacio & Carreras, Francesc, 1996. "The Owen Value Applied to Games with Graph-Restricted Communication," Games and Economic Behavior, Elsevier, vol. 12(1), pages 42-53, January.
    12. Silvia Lorenzo-Freire, 2017. "New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 579-600, October.
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    More about this item

    Keywords

    TU-game; Owen graph value; Consistency; Reduced game; Banzhaf value;
    All these keywords.

    JEL classification:

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

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