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Technical note: Characterization of binomial semivalues through delegation games

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  • Rafael Amer
  • José Miguel Giménez

Abstract

Semivalues are allocation rules for cooperative games that assign to each player in a given game a weighted sum of his marginal contributions to all coalitions he belongs to, where the weighting coefficients depend only on the coalition size. Binomial semivalues are a special class of semivalues whose weighting coefficients are obtained by means of a unique parameter. In particular, the Banzhaf value is a binomial semivalue. In this article, we provide an axiomatic characterization for each binomial semivalue. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

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  • Rafael Amer & José Miguel Giménez, 2007. "Technical note: Characterization of binomial semivalues through delegation games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 702-708, September.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:6:p:702-708
    DOI: 10.1002/nav.20238
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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. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
    3. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    4. Rafael Amer & José Miguel giménez, 2003. "Modification of Semivalues for Games with Coalition Structures," Theory and Decision, Springer, vol. 54(3), pages 185-205, May.
    5. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 179-186.
    6. 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.
    7. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
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