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 ones and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms.
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- repec:oup:restud:v:73:y:2006:i:4:p:849-868 is not listed on IDEAS
- Masahiro Kumabe & H. Reiju Mihara, 2008.
"The Nakamura numbers for computable simple games,"
Social Choice and Welfare,
Springer, vol. 31(4), pages 621-640, December.
- Mihara, H.R., 1994.
"Arrow's Theorem and Turing Computability,"
276, Minnesota - Center for Economic Research.
- Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003.
"Social Choice and Electoral Competition in the General Spatial Model,"
IDEI Working Papers
188, Institut d'Économie Industrielle (IDEI), Toulouse.
- Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
- Nabil I. Al-Najjar & Luca Anderlini & Leonardo Felli, 2003.
CESifo Working Paper Series
1092, CESifo Group Munich.
- Kumabe, Masahiro & Mihara, H. Reiju, 2008.
"Preference aggregation theory without acyclicity: The core without majority dissatisfaction,"
11728, University Library of Munich, Germany.
- Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," Games and Economic Behavior, Elsevier, vol. 72(1), pages 187-201, May.
- Luca Anderlini & Leonardo Felli, 1994. "Incomplete Written Contracts: Undescribable States of Nature," The Quarterly Journal of Economics, Oxford University Press, vol. 109(4), pages 1085-1124.
- Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
- Mihara, H. Reiju, 2004.
"Nonanonymity and sensitivity of computable simple games,"
Mathematical Social Sciences,
Elsevier, vol. 48(3), pages 329-341, November.
- H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004.
- Shanfeng Zhu & Xiaotie Deng & Maocheng Cai & Qizhi Fang, 2002. "On computational complexity of membership test in flow games and linear production games," International Journal of Game Theory, Springer, vol. 31(1), pages 39-45.
- Peleg, Bezalel, 2002.
"Game-theoretic analysis of voting in committees,"
Handbook of Social Choice and Welfare,
in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 8, pages 395-423
- Mihara, H. Reiju, 1999. "Arrow's theorem, countably many agents, and more visible invisible dictators1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 267-287, November.
- H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997.
- Kumabe, Masahiro & Mihara, H. Reiju, 2008.
"Computability of simple games: A characterization and application to the core,"
Journal of Mathematical Economics,
Elsevier, vol. 44(3-4), pages 348-366, February.
- Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
- Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
- Lewis, Alain A., 1988. "An infinite version of arrow's theorem in the effective setting," Mathematical Social Sciences, Elsevier, vol. 16(1), pages 41-48, August.
- Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
- William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer, vol. 18(2), pages 327-386.
- Weber, Robert J., 1994. "Games in coalitional form," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 36, pages 1285-1303 Elsevier.
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