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Growth of dimension in complete simple games

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  • O’Dwyer, Liam
  • Slinko, Arkadii

Abstract

Using a novel technique of Kurz and Napel (2015), we demonstrate that the worst-case growth of dimension in complete simple games is exponential in the number of players. We also prove that roughly-weighted games of arbitrary dimension exist.

Suggested Citation

  • O’Dwyer, Liam & Slinko, Arkadii, 2017. "Growth of dimension in complete simple games," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 2-8.
    • Handle: RePEc:eee:matsoc:v:90:y:2017:i:c:p:2-8
    DOI: 10.1016/j.mathsocsci.2016.08.008
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    References listed on IDEAS

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    1. Deineko, Vladimir G. & Woeginger, Gerhard J., 2006. "On the dimension of simple monotonic games," European Journal of Operational Research, Elsevier, vol. 170(1), pages 315-318, April.
    2. Ali Hameed & Arkadii Slinko, 2015. "Roughly weighted hierarchical simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 295-319, May.
    3. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650.
    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. J. Freixas, 1997. "Different ways to represent weighted majority games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 5(2), pages 201-211, December.
    7. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
    8. Freixas, J., 2004. "The dimension for the European Union Council under the Nice rules," European Journal of Operational Research, Elsevier, vol. 156(2), pages 415-419, July.
    9. Josep Freixas & Dorota Marciniak, 2009. "A minimum dimensional class of simple games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 407-414, December.
    10. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
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    Cited by:

    1. Kurz, Sascha, 2021. "A note on the growth of the dimension in complete simple games," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 14-18.
    2. Molinero, Xavier & Riquelme, Fabián & Roura, Salvador & Serna, Maria, 2023. "On the generalized dimension and codimension of simple games," European Journal of Operational Research, Elsevier, vol. 306(2), pages 927-940.

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