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

Masahiro Kumabe and H. Reiju Mihara

Journal of Mathematical Economics, 2011, vol. 47, issue 2, pages 150-158

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.

Keywords: Voting; games; Axiomatic; method; Complete; independence; Turing; computability; Multi-criterion; decision-making (search for similar items in EconPapers)
Date: 2011
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Working Paper: Computability of simple games: A complete investigation of the sixty-four possibilities (2006)
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Persistent link: http://EconPapers.repec.org/RePEc:eee:mateco:v:47:y:2011:i:2:p:150-158

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