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On the core, the Weber set and convexity in games with a priori unions

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  • Pulido, Manuel A.
  • Sánchez-Soriano, Joaquín

Abstract

This paper deals with the concepts of core and Weber set with a priori unions à la Owen. As far as we know, the Owen approach to games with a priori unions has never been studied from the coalitional stability point of view. Thus we introduce the coalitional core and coalitional Weber set and characterize the class of convex games with a priori unions by means of the relationships between both solution concepts.

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  • Pulido, Manuel A. & Sánchez-Soriano, Joaquín, 2009. "On the core, the Weber set and convexity in games with a priori unions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 468-475, March.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:2:p:468-475
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    1. 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.
    2. Carreras, Francesc & García Jurado, Ignacio & Pacios, Miguel A., 1992. "Estudio coalicional de los parlamentos autonómicos españoles de régimen común," DE - Documentos de Trabajo. Economía. DE 3026, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    4. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    5. Albizuri, M.J. & Aurrecoechea, J. & Zarzuelo, J.M., 2006. "Configuration values: Extensions of the coalitional Owen value," Games and Economic Behavior, Elsevier, vol. 57(1), pages 1-17, October.
    6. Carreras, Francesc & Owen, Guillermo, 1988. "Evaluation of the Catalonian Parliament, 1980-1984," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 87-92, February.
    7. Pulido, Manuel A. & Sanchez-Soriano, Joaquin, 2006. "Characterization of the core in games with restricted cooperation," European Journal of Operational Research, Elsevier, vol. 175(2), pages 860-869, December.
    8. 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).
    9. Curiel, I. & Tijs, S.H., 1991. "Minimarg and the maximarg operators," Other publications TiSEM 1f024ef6-4383-41ae-aba6-0, Tilburg University, School of Economics and Management.
    10. 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.
    11. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    12. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    13. Vazquez-Brage, M. & van den Nouweland, A. & Garcia-Jurado, I., 1997. "Owen's coalitional value and aircraft landing fees," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 273-286, October.
    14. 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.
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