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The Multilinear Extension and the Symmetric Coalition Banzhaf Value

Author

Listed:
  • J. Alonso-Meijide
  • F. Carreras
  • M. Fiestras-Janeiro

Abstract

Alonso-Meijide and Fiestras-Janeiro (2002, Annals of Operations Research 109, 213–227) proposed a modification of the Banzhaf value for games where a coalition structure is given. In this paper we present a method to compute this value by means of the multilinear extension of the game. A real-world numerical example illustrates the application procedure. Copyright Springer 2005

Suggested Citation

  • J. Alonso-Meijide & F. Carreras & M. Fiestras-Janeiro, 2005. "The Multilinear Extension and the Symmetric Coalition Banzhaf Value," Theory and Decision, Springer, vol. 59(2), pages 111-126, September.
    • Handle: RePEc:kap:theord:v:59:y:2005:i:2:p:111-126
    DOI: 10.1007/s11238-005-0944-x
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    References listed on IDEAS

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    1. Annick Laruelle, 1999. "- On The Choice Of A Power Index," Working Papers. Serie AD 1999-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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    Citations

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    Cited by:

    1. Michael Jones & Jennifer Wilson, 2013. "Two-step coalition values for multichoice games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 65-99, February.
    2. László Á. Kóczy & Miklós Pintér, 2011. "The men who weren't even there: Legislative voting with absentees," Working Paper Series 1104, Óbuda University, Keleti Faculty of Business and Management.
    3. J. Alonso-Meijide & B. Casas-Méndez & A. González-Rueda & S. Lorenzo-Freire, 2014. "Axiomatic of the Shapley value of a game with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 749-770, July.
    4. Michael Jones & Jennifer Wilson, 2010. "Multilinear extensions and values for multichoice games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 145-169, August.
    5. Carreras, Francesc & Giménez, José Miguel, 2011. "Power and potential maps induced by any semivalue: Some algebraic properties and computation by multilinear extensions," European Journal of Operational Research, Elsevier, vol. 211(1), pages 148-159, May.
    6. Carreras, Francesc & Puente, María Albina, 2015. "Coalitional multinomial probabilistic values," European Journal of Operational Research, Elsevier, vol. 245(1), pages 236-246.
    7. J. Alonso-Meijide & C. Bowles & M. Holler & S. Napel, 2009. "Monotonicity of power in games with a priori unions," Theory and Decision, Springer, vol. 66(1), pages 17-37, January.
    8. J. Alonso-Meijide & B. Casas-Méndez & M. Fiestras-Janeiro & M. Holler, 2011. "The Deegan–Packel index for simple games with a priori unions," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(2), pages 425-439, February.
    9. José Giménez & María Puente, 2015. "A method to calculate generalized mixed modified semivalues: application to the Catalan Parliament (legislature 2012–2016)," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 669-684, October.
    10. Francesc Carreras & María Albina Puente, 2012. "Symmetric Coalitional Binomial Semivalues," Group Decision and Negotiation, Springer, vol. 21(5), pages 637-662, September.

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    More about this item

    Keywords

    coalition structure; Banzhaf value; coalition value; multi-linear extension; C71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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