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Three hierarchies of simple games parameterized by “resource” parameters

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  • Tatiana Gvozdeva
  • Lane Hemaspaandra
  • Arkadii Slinko

Abstract

This paper contributes to the program of numerical characterization and classification of simple games outlined in the classic monograph of von Neumann and Morgenstern. We suggest three possible ways to classify simple games beyond the classes of weighted and roughly weighted games. To this end we introduce three hierarchies of games and prove some relationships between their classes. We prove that our hierarchies are true (i.e., infinite) hierarchies. In particular, they are strict in the sense that more of the key “resource” (which may, for example, be the size or structure of the “tie-breaking” region where the weights of the different coalitions are considered so close that we are allowed to specify either winningness or nonwinningness of the coalition) yields the flexibility to capture strictly more games. Copyright Springer-Verlag 2013

Suggested Citation

  • Tatiana Gvozdeva & Lane Hemaspaandra & Arkadii Slinko, 2013. "Three hierarchies of simple games parameterized by “resource” parameters," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 1-17, February.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:1:p:1-17
    DOI: 10.1007/s00182-011-0308-4
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    References listed on IDEAS

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    1. 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.
    2. Gvozdeva, Tatiana & Slinko, Arkadii, 2011. "Weighted and roughly weighted simple games," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 20-30, January.
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    Cited by:

    1. Akihiro Kawana & Tomomi Matsui, 2022. "Trading transforms of non-weighted simple games and integer weights of weighted simple games," Theory and Decision, Springer, vol. 93(1), pages 131-150, July.

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