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Nonanonymity and sensitivity of computable simple games

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Author Info
H. Reiju Mihara (Kagawa University)

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Abstract

This paper investigates algorithmic computability of simple games (voting games). It shows that (i) games with a finite carrier are computable, (ii) computable games have both finite winning coalitions and cofinite losing coalitions, and (iii) computable games violate any conceivable notion of anonymity, including finite anonymity and measurebased anonymity. The paper argues that computable games are excluded from the intuitive class of gniceh infinite games, employing the notion of ginsensitivityh\-equal treatment of any two coalitions that differ only on a finite set.

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File URL: http://129.3.20.41/eps/game/papers/0310/0310006.pdf
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Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 0310006.

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Length: 15 pages
Date of creation: 31 Oct 2003
Date of revision: 01 Jun 2004
Handle: RePEc:wpa:wuwpga:0310006

Note: Type of Document - pdf; prepared on Mac OS X; pages: 15; To appear in Mathematical Social Sciences figures: None
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Web page: http://129.3.20.41

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Related research
Keywords: Voting games infinitely many players ultrafilters recursion theory Turing computability finite carriers finite winning coalitions algorithms

Other versions of this item:

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
C69 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Other

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM. [Downloadable!]
    Other versions:
  2. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276. [Downloadable!] (restricted)
    Other versions:
  3. 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 Elsevier. [Downloadable!] (restricted)
  4. H. Reiju Mihara, 1997. "Anonymity and neutrality in Arrow's Theorem with restricted coalition algebras," Social Choice and Welfare, Springer, vol. 14(4), pages 503-512. [Downloadable!] (restricted)
    Other versions:
  5. 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. [Downloadable!]
    Other versions:
  6. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997. [Downloadable!]
    Other versions:
  9. Armstrong, Thomas E., 1985. "Precisely dictatorial social welfare functions : Erratum and Addendum to `arrows theorem with restricted coalition algebras'," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 57-59, February. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany. [Downloadable!]
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