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

Masahiro Kumabe and H. Reiju Mihara

MPRA Paper from University Library of Munich, Germany

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

Keywords: Voting games; infinitely many players; axiomatic method; complete independence; algorithms; Turing computability; recursion theory (search for similar items in EconPapers)
JEL-codes: D90 C69 D71 C71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2006-10
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https://mpra.ub.uni-muenchen.de/440/1/MPRA_paper_440.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/4405/1/MPRA_paper_4405.pdf revised version (application/pdf)
https://mpra.ub.uni-muenchen.de/29000/1/MPRA_paper_29000.pdf revised version (application/pdf)

Related works:
Journal Article: Computability of simple games: A complete investigation of the sixty-four possibilities (2011) Downloads
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