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A Parametric Family of Mixed Coalitional Values

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Recent Advances in Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 563))

Summary

We introduce here a family of mixed coalitional values. They extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the Shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.

Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics II and Industrial Engineering School of Terrassa, Polytechnic University of Catalonia, Spain

    Francesc Carreras

  2. Department of Applied Mathematics III and Polytechnic School of Manresa, Polytechnic University of Catalonia, Spain

    María Albina Puente

Authors
  1. Francesc Carreras
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  2. María Albina Puente
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Avignon, 33, rue Louis Pasteur, 84000, Avignon, France

    Alberto Seeger

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© 2006 Springer-Verlag Berlin Heidelberg

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Carreras, F., Puente, M.A. (2006). A Parametric Family of Mixed Coalitional Values. In: Seeger, A. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28258-0_20

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