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Complete games with minimum

Author

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  • J. Freixas
  • M.A. Puente

Abstract

Some real-world examples of simple games, like the procedure to amend the Canadian Constitution, are complete simple games with minimum. Using characteristic invariants for this class of games, we study different types of solution concepts. For an arbitrary number of players we get the nucleolus by means of a determinate compatible system of equations, characterize the maximality of the kernel and give a method to calculate semivalues. Several applications are found at the end of the paper. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • J. Freixas & M.A. Puente, 1998. "Complete games with minimum," Annals of Operations Research, Springer, vol. 84(0), pages 97-109, December.
    • Handle: RePEc:spr:annopr:v:84:y:1998:i:0:p:97-109:10.1023/a:1018905407647
    DOI: 10.1023/A:1018905407647
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    Citations

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    Cited by:

    1. Josep Freixas & Sascha Kurz, 2014. "Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum," Annals of Operations Research, Springer, vol. 222(1), pages 317-339, November.
    2. Freixas, Josep & Kurz, Sascha, 2013. "The golden number and Fibonacci sequences in the design of voting structures," European Journal of Operational Research, Elsevier, vol. 226(2), pages 246-257.
    3. Josep Freixas & Marc Freixas & Sascha Kurz, 2017. "On the characterization of weighted simple games," Theory and Decision, Springer, vol. 83(4), pages 469-498, December.
    4. Freixas, Josep & Puente, Maria Albina, 2008. "Dimension of complete simple games with minimum," European Journal of Operational Research, Elsevier, vol. 188(2), pages 555-568, July.
    5. Gvozdeva, Tatiana & Hameed, Ali & Slinko, Arkadii, 2013. "Weightedness and structural characterization of hierarchical simple games," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 181-189.
    6. Maria Axenovich & Sonali Roy, 2010. "On the structure of minimal winning coalitions in simple voting games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 429-440, March.
    7. Carreras, Francesc & Freixas, Josep, 2004. "A power analysis of linear games with consensus," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 207-221, September.

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