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A Banzhaf share function for cooperative games in coalition structure

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  • Gerard van der Laan

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  • René van den Brink

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Abstract

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Suggested Citation

  • 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.
  • Handle: RePEc:kap:theord:v:53:y:2002:i:1:p:61-86
    DOI: 10.1023/A:1020805106965
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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    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.
    3. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    4. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    5. 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.
    6. 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.
    7. 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.
    8. Owen, Guillermo & Winter, Eyal, 1992. "The multilinear extension and the coalition structure value," Games and Economic Behavior, Elsevier, vol. 4(4), pages 582-587, October.
    9. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    10. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    11. van den Brink, J.R. & van der Laan, G., 1998. "The Normalized Banzhaf Value and the Banzhaf Share Function," Research Memorandum 764, Tilburg University, School of Economics and Management.
    12. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 567-582.
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    Citations

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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    2. 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.
    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.
    4. 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.
    5. Nicola G. Andjiga & Sebastien Courtin, 2013. "Coalition configurations and share functions," Working Papers hal-00914883, HAL.
    6. Kongo, Takumi, 2011. "Value of games with two-layered hypergraphs," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 114-119, September.
    7. repec:hal:journl:halshs-00344457 is not listed on IDEAS
    8. Nicolas G. Andjiga & Sébastien Courtin, 2015. "Coalition configurations and share functions," Post-Print hal-00914883, HAL.

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