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The axiomatic approach to three values in games with coalition structure

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Author Info
Gómez-Rúa, María
Vidal-Puga, Juan

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Abstract

We study three values for transferable utility games with coalition structure, including the Owen coalitional value and two weighted versions with weights given by the size of the coalitions. We provide three axiomatic characterizations using the properties of Efficiency, Linearity, Independence of Null Coalitions, and Coordination, with two versions of Balanced Contributions inside a Coalition and Weighted Sharing in Unanimity Games, respectively.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8904.

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Date of creation: 29 May 2008
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Handle: RePEc:pra:mprapa:8904

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Related research
Keywords: coalition structure; coalitional value;

Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
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  3. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July. [Downloadable!] (restricted)
  4. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November. [Downloadable!] (restricted)
  5. Gérard Hamiache, 2001. "The Owen value values friendship," International Journal of Game Theory, Springer, vol. 29(4), pages 517-532. [Downloadable!] (restricted)
  6. Chae, Suchan & Heidhues, Paul, 2004. "A group bargaining solution," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 37-53, July. [Downloadable!] (restricted)
  7. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August. [Downloadable!] (restricted)
  8. Gustavo Bergantiños & Balbina Casas- Méndez & Gloria Fiestras- Janeiro & Juan Vidal-Puga, 2005. "A Focal-Point Solution for Bargaining Problems with Coalition Structure," Game Theory and Information 0511006, EconWPA. [Downloadable!]
  9. R. Amer & F. Carreras, 1995. "Cooperation indices and coalitional value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 3(1), pages 117-135, June. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer, vol. 18(2), pages 227-40.
  12. Marcin Malawski, 2004. "``Counting'' power indices for games with a priori unions," Theory and Decision, Springer, vol. 56(2_2), pages 125-140, 02. [Downloadable!]
  13. Albizuri, M. Josune & Zarzuelo, Jose M., 2004. "On coalitional semivalues," Games and Economic Behavior, Elsevier, vol. 49(2), pages 221-243, November. [Downloadable!] (restricted)
  14. Juan Vidal-Puga, 2005. "The Harsanyi paradox and the 'right to talk' in bargaining among coalitions," Game Theory and Information 0501005, EconWPA. [Downloadable!]
  15. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  16. Ruiz, Luis M & Valenciano, Federico & Zarzuelo, Jose M, 1996. "The Least Square Prenucleolus and the Least Square Nucleolus. Two Values for TU Games Based on the Excess Vector," International Journal of Game Theory, Springer, vol. 25(1), pages 113-34.
  17. 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. [Downloadable!] (restricted)
  18. Gustavo Bergantiños & Juan Vidal-Puga, 2003. "The NTU consistent coalitional value," Game Theory and Information 0303007, EconWPA. [Downloadable!]
  19. Albizuri, M.J., 2008. "Axiomatizations of the Owen value without efficiency," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 78-89, January. [Downloadable!] (restricted)
  20. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June. [Downloadable!] (restricted)
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