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Coalition configurations and share functions

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  • Nicolas Andjiga
  • Sebastien Courtin

Abstract

Albizuri and Aurrekoetxea (Soc Choice Welf 26:571–596, 2006a ) and Albizuri et al. (Games Econ Behav 57:1–17, 2006b ) defined values for games in which the players are organized into an a priori coalition configuration. In games with coalition configuration, we suppose that players organize themselves into coalitions that are not necessarily disjoint. A player can belong to more than one a priori coalition. In this paper we redefine coalition configuration values by using the concept of share function, as introduced by van der Laan and van den Brink (Theory Decis 53:61–86, 2002 ). A share function assigns to every player in a game its share in the worth to be distributed. We also define and characterize a general class of share function for games with coalition configuration which contains among other values those introduced by Albizuri et al. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Nicolas Andjiga & Sebastien Courtin, 2015. "Coalition configurations and share functions," Annals of Operations Research, Springer, vol. 225(1), pages 3-25, February.
    • Handle: RePEc:spr:annopr:v:225:y:2015:i:1:p:3-25:10.1007/s10479-014-1754-8
    DOI: 10.1007/s10479-014-1754-8
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    References listed on IDEAS

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    1. M. J. Albizuri, 2001. "An axiomatization of the modified Banzhaf Coleman index," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 167-176.
    2. Gerard van der Laan & René van den Brink, 2002. "A Banzhaf share function for cooperative games in coalition structure," Theory and Decision, Springer, vol. 53(1), pages 61-86, August.
    3. 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.
    4. 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).
    5. 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.
    6. van den Brink, Rene & van der Laan, Gerard, 2005. "A class of consistent share functions for games in coalition structure," Games and Economic Behavior, Elsevier, vol. 51(1), pages 193-212, April.
    7. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
    8. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    9. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    10. Gerard van der Laan & René van den Brink, 1998. "Axiomatization of a class of share functions for n-person games," Theory and Decision, Springer, vol. 44(2), pages 117-148, April.
    11. 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.
    12. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    13. M. Albizuri & Jesus Aurrekoetxea, 2006. "Coalition Configurations and the Banzhaf Index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 571-596, June.
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    Cited by:

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    3. Sébastien Courtin, 2011. "Power in the European Union: an evaluation according to a priori relations between states," Economics Bulletin, AccessEcon, vol. 31(1), pages 534-545.
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    5. Álvarez-Mozos, M. & van den Brink, R. & van der Laan, G. & Tejada, O., 2013. "Share functions for cooperative games with levels structure of cooperation," European Journal of Operational Research, Elsevier, vol. 224(1), pages 167-179.
    6. Dan C. Popescu & Philip Kilby, 2020. "Approximation of the Shapley value for the Euclidean travelling salesman game," Annals of Operations Research, Springer, vol. 289(2), pages 341-362, June.

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    More about this item

    Keywords

    Coalition configuration; Coalition structure; Share function; Shapley value; Banzhaf value; C70; C71; D7;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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