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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

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 algorithmic 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 ones and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 2 (March)
Pages: 150-158

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Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:150-158

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Voting games Axiomatic method Complete independence Turing computability Multi-criterion decision-making;

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References

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Cited by:
  1. 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.
  2. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "The Nakamura numbers for computable simple games," MPRA Paper 3684, University Library of Munich, Germany.

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