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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 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.

Suggested Citation

  • Gómez-Rúa, María & Vidal-Puga, Juan, 2008. "The axiomatic approach to three values in games with coalition structure," MPRA Paper 8904, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:8904
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    References listed on IDEAS

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    1. Albizuri, M. Josune & Zarzuelo, Jose M., 2004. "On coalitional semivalues," Games and Economic Behavior, Elsevier, vol. 49(2), pages 221-243, November.
    2. Levy, Anat & Mclean, Richard P., 1989. "Weighted coalition structure values," Games and Economic Behavior, Elsevier, vol. 1(3), pages 234-249, September.
    3. Tasos Kalandrakis, 2006. "Proposal Rights and Political Power," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 441-448, April.
    4. Gustavo Bergantiños & Juan Vidal-Puga, 2005. "The Consistent Coalitional Value," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 832-851, November.
    5. 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.
    6. Haeringer, Guillaume, 2006. "A new weight scheme for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 88-98, July.
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    9. Albizuri, M.J., 2008. "Axiomatizations of the Owen value without efficiency," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 78-89, January.
    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.
    11. 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.
    12. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
    13. Gustavo Bergantiños & Juan Vidal-Puga, 2003. "The NTU consistent coalitional value," Game Theory and Information 0303007, University Library of Munich, Germany.
    14. Marcin Malawski, 2004. "‘‘Counting’’ power indices for games with a priori unions," Theory and Decision, Springer, vol. 56(1), pages 125-140, April.
    15. Winter, Eyal, 1991. "On Non-transferable Utility Games with Coalition Structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(1), pages 53-63.
    16. 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.
    17. 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.
    18. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
    19. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
    20. Gérard Hamiache, 2001. "The Owen value values friendship," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 517-532.
    21. Marcin Malawski, 2004. "``Counting'' power indices for games with a priori unions," Theory and Decision, Springer, vol. 56(2_2), pages 125-140, February.
    22. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, September.
    23. R. Amer & F. Carreras, 1995. "Cooperation indices and coalitional value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 117-135, June.
    24. 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.
    25. 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.
    26. Tadeusz Radzik & Andrzej Nowak & Theo Driessen, 1997. "Weighted Banzhaf values," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 109-118, February.
    27. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    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. Bergantinos, G. & Casas-Mendez, B. & Fiestras-Janeiro, M.G. & Vidal-Puga, J.J., 2007. "A solution for bargaining problems with coalition structure," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 35-58, July.
    30. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    31. Francesc Carreras & María Albina Puente, 2006. "A Parametric Family of Mixed Coalitional Values," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 323-339, Springer.
    32. Chae, Suchan & Heidhues, Paul, 2004. "A group bargaining solution," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 37-53, July.
    33. Andrzej S. Nowak & Tadeusz Radzik, 2000. "note: An alternative characterization of the weighted Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 127-132.
    34. 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.
    35. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    36. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    37. 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;Game Theory Society, vol. 25(1), pages 113-134.
    38. 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, University Library of Munich, Germany.
    39. 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.
    40. 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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    Keywords

    coalition structure; coalitional value;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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