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A coalitional value for games on convex geometries with a coalition structure

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  • Meng, Fanyong
  • Chen, Xiaohong
  • Zhang, Qiang

Abstract

With respect to games on convex geometries with a coalition structure, a coalitional value named the generalized symmetric coalitional Banzhaf value is defined, which can be seen as an extension of the symmetric coalitional Banzhaf value given by Alonso-Meijide and Fiestrs-Janeiro and the Shapley value for games on convex geometries introduced by Bilbao. Based on the established axiomatic system, the existence and uniqueness of the given coalitional value is shown. Meanwhile, a special case is briefly studied.

Suggested Citation

  • Meng, Fanyong & Chen, Xiaohong & Zhang, Qiang, 2015. "A coalitional value for games on convex geometries with a coalition structure," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 605-614.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:605-614
    DOI: 10.1016/j.amc.2015.05.110
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    References listed on IDEAS

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    1. 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.
    2. J. M. Bilbao & T. S. H. Driessen & A. Jiménez-Losada & E. Lebrón, 2002. "The Shapley value for games on matroids: The dynamic model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 287-301, November.
    3. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Discussion Paper 1999-20, Tilburg University, Center for Economic Research.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. Bilbao, J. M., 1998. "Axioms for the Shapley value on convex geometries," European Journal of Operational Research, Elsevier, vol. 110(2), pages 368-376, October.
    6. J. Bilbao & A. Jiménez-Losada & E. Lebrón & S. Tijs, 2002. "Theτ-value for games on matroids," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 67-81, June.
    7. Albizuri, M.J., 2008. "Axiomatizations of the Owen value without efficiency," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 78-89, January.
    8. Amer, Rafael & Carreras, Francese & Gimenez, Jose Miguel, 2002. "The modified Banzhaf value for games with coalition structure: an axiomatic characterization," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 45-54, January.
    9. Hamiache, Gerard, 1999. "A new axiomatization of the Owen value for games with coalition structures," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 281-305, May.
    10. 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.
    11. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Other publications TiSEM 4f162187-3069-4cb5-8353-5, Tilburg University, School of Economics and Management.
    12. E. Algaba & J. M. Bilbao & R. van den Brink & A. Jiménez-Losada, 2003. "Axiomatizations of the Shapley value for cooperative games on antimatroids," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 49-65, April.
    13. 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.
    14. M. Albizuri, 2009. "The multichoice coalition value," Annals of Operations Research, Springer, vol. 172(1), pages 363-374, November.
    15. 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.
    16. J. M. Bilbao & T. S. H. Driessen & A. Jiménez Losada & E. Lebrón, 2001. "The Shapley value for games on matroids: The static model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(2), pages 333-348, June.
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