Kumabe, Masahiro and Mihara, H. Reiju (2011): Computability of simple games: A complete investigation of the sixtyfour 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 sixtyfour 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.
Item Type:  MPRA Paper 

Original Title:  Computability of simple games: A complete investigation of the sixtyfour possibilities 
Language:  English 
Keywords:  Voting games; axiomatic method; complete independence; Turing computability; multicriterion decisionmaking 
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 DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69  Other 
Item ID:  29000 
Depositing User:  H. Reiju Mihara 
Date Deposited:  20 Feb 2011 20:21 
Last Modified:  28 Sep 2019 22:53 
References:  AlNa jjar, N. I., Anderlini, L., Felli, L., 2006. Undescribable events. Review of Economic Studies 73, 849–868. Arrow, K. J., 1963. Social Choice and Individual Values, 2nd Edition. Yale University Press, New Haven. Bartholdi, J., III, Tovey, C. A., Trick, M. A., 1989a. Voting schemes for which it can be diﬃcult to tell who won the election. Social Choice and Welfare 6, 157–165. Bartholdi, J. J., III, Tovey, C. A., Trick, M. A., 1989b. The computational diﬃculty of manipulating an election. Social Choice and Welfare 6, 227–241. Kelly, J. S., 1988. Social choice and computational complexity. Journal of Mathematical Economics 17, 1–8. Kumabe, M., Mihara, H. R., Aug. 2007. Computability of simple games: A complete investigation of the sixtyfour possibilities. MPRA Paper 4405, Munich University Library, http://mpra.ub.unimuenchen.de/4405/ Kumabe, M., Mihara, H. R., 2008a. Computability of simple games: A characterization and application to the core. Journal of Mathematical Economics 44, 348–366. Kumabe, M., Mihara, H. R., 2008b. The Nakamura numbers for computable simple games. Social Choice and Welfare 31, 621–640. Kumabe, M., Mihara, H. R., 2010. Preference aggregation theory without acyclicity: The core without ma jority dissatisfaction. Games and Economic Behavior, Doi:10.1016/j.geb.2010.06.008 Lewis, A. A., 1988. An inﬁnite version of Arrow’s Theorem in the effective setting. Mathematical Social Sciences 16, 41–48. May, K. O., 1952. A set of independent, necessary and suﬃcient conditions for simple ma jority decision. Econometrica 20, 680–84. May, K. O., 1953. A note on the complete independence of the conditions for simple ma jority decision. Econometrica 21, 172–173. Mihara, H. R., 1997. Arrow’s Theorem and Turing computability. Economic Theory 10, 257–76. Mihara, H. R., 1999. Arrow’s theorem, countably many agents, and more visible invisible dictators. Journal of Mathematical Economics 32, 267–287. Mihara, H. R., 2004. Nonanonymity and sensitivity of computable simple games. Mathematical Social Sciences 48, 329–341. Odifreddi, P., 1992. Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers. Elsevier, Amsterdam. Peleg, B., 2002. Gametheoretic analysis of voting in committees. In: Arrow, K. J., Sen, A. K., Suzumura, K. (Eds.), Handbook of Social Choice and Welfare. Vol. 1. Elsevier, Amsterdam, Ch. 8, pp. 395–423. Soare, R. I., 1987. Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets. SpringerVerlag, Berlin. Thomson, W., 2001. On the axiomatic method and its recent applications to game theory and resource allocation. Social Choice and Welfare 18, 327–386. Weber, R. J., 1994. Games in coalitional form. In: Aumann, R. J., Hart, S. (Eds.), Handbook of Game Theory. Vol. 2. Elsevier, Amsterdam, Ch. 36, pp. 1285–1303. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/29000 
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Computability of simple games: A complete investigation of the sixtyfour possibilities. (deposited 13 Oct 2006)

Computability of simple games: A complete investigation of the sixtyfour possibilities. (deposited 09 Aug 2007)
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Computability of simple games: A complete investigation of the sixtyfour possibilities. (deposited 09 Aug 2007)