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

Kumabe, Masahiro and Mihara, H. Reiju (2007): Computability of simple games: A complete investigation of the sixty-four possibilities.

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

• Item Type: MPRA Paper
• Language: English
• Keywords: Voting games; axiomatic method; complete independence; Turing computability; legal precedents
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; D - Microeconomics > D9 - Intertemporal Choice > D90 - General; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69 - Other

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