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

Kumabe, Masahiro and Mihara, H. Reiju (2011): Computability of simple games: A complete investigation of the sixty-four possibilities. Forthcoming in: Journal of Mathematical Economics

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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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