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The axiomatic approach to three values in games with coalition structure

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  • Gómez-Rúa, María
  • Vidal-Puga, Juan

Abstract

We present a unified framework for a broad class of values in 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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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 207 (2010)
Issue (Month): 2 (December)
Pages: 795-806

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Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:795-806

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Coalition structure Coalitional value Axiomatic approach;

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References

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  1. 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.
  2. Gómez-Rúa, María & Vidal-Puga, Juan, 2008. "Balanced per capita contributions and levels structure of cooperation," MPRA Paper 8208, University Library of Munich, Germany.
  3. Marcin Malawski, 2004. "``Counting'' power indices for games with a priori unions," Theory and Decision, Springer, vol. 56(2_2), pages 125-140, 02.
  4. Juan Vidal-Puga, 2005. "The Harsanyi paradox and the 'right to talk' in bargaining among coalitions," Game Theory and Information 0501005, EconWPA.
  5. Haeringer, Guillaume, 2006. "A new weight scheme for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 88-98, July.
  6. Gérard Hamiache, 2001. "The Owen value values friendship," International Journal of Game Theory, Springer, vol. 29(4), pages 517-532.
  7. Albizuri, M.J., 2008. "Axiomatizations of the Owen value without efficiency," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 78-89, January.
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  9. 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.
  10. 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.
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  23. Gustavo Bergantiños & Juan Vidal-Puga, 2003. "The NTU consistent coalitional value," Game Theory and Information 0303007, EconWPA.
  24. Marcin Malawski, 2004. "‘‘Counting’’ power indices for games with a priori unions," Theory and Decision, Springer, vol. 56(1), pages 125-140, April.
  25. Lorenzo-Freire, Silvia & Alonso-Meijide, Jose M. & Casas-Mendez, Balbina & Hendrickx, Ruud, 2007. "Balanced contributions for TU games with awards and applications," European Journal of Operational Research, Elsevier, vol. 182(2), pages 958-964, October.
  26. 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.
  27. 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.
  28. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  29. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
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  32. 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.
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Citations

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Cited by:
  1. Juan Vidal-Puga, 2005. "The Harsanyi paradox and the 'right to talk' in bargaining among coalitions," Game Theory and Information 0501005, EconWPA.
  2. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
  3. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
  4. Gómez-Rúa, María & Vidal-Puga, Juan, 2008. "Balanced per capita contributions and levels structure of cooperation," MPRA Paper 8208, University Library of Munich, Germany.

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