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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 437.

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Date of creation: Jul 2006
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Handle: RePEc:pra:mprapa:437

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

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References

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  23. 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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Citations

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Cited by:
  1. 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.
  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, vol. 31(4), pages 621-640, December.
  4. 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.

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