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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 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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 440.

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Date of creation: Feb 2011
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Handle: RePEc:pra:mprapa:440

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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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  10. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
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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, vol. 31(4), pages 621-640, December.

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