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

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

2011-02-20

arxiv.org/abs/1102.4037v1

Journal of Mathematical Economics 47 (2011) 150-158

Computer Science

Computer Science and Game Theory

25 pages

Scientific paper

10.1016/j.jmateco.2010.12.003

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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