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Computability of simple games: A complete investigation of the sixty-four possibilities

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  • Kumabe, Masahiro
  • Mihara, H. Reiju

Abstract

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable infinitegames and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms.

Suggested Citation

  • Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:440
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    Cited by:

    1. Masahiro Kumabe & H. Reiju Mihara, 2008. "The Nakamura numbers for computable simple games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 621-640, December.
    2. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 348-366, February.

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    More about this item

    Keywords

    Voting games; infinitely many players; axiomatic method; complete independence; algorithms; Turing computability; recursion theory;
    All these keywords.

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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