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Computability of simple games: A characterization and application to the core

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  • Kumabe, Masahiro
  • Mihara, H. Reiju

Abstract

It was shown earlier that the class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games, strengthens the earlier result that computable games violate anonymity, and gives examples showing that the above inclusions are strict. It also extends Nakamura’s theorem about the nonemptyness of the core and shows that computable simple games have a finite Nakamura number, implying that the number of alternatives that the players can deal with rationally is restricted.

Suggested Citation

  • Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:437
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    References listed on IDEAS

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    Cited by:

    1. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," Games and Economic Behavior, Elsevier, vol. 72(1), pages 187-201, May.
    2. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Computability of simple games: A complete investigation of the sixty-four possibilities," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 150-158, March.
    3. 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.
    4. 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.
    5. Koji Takamiya & Akira Tanaka, 2016. "Computational complexity in the design of voting rules," Theory and Decision, Springer, vol. 80(1), pages 33-41, January.

    More about this item

    Keywords

    Voting games; infinitely many players; recursion theory; Turingcomputability; computable manuals and contracts;

    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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