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Nonanonymity and sensitivity of computable simple games

  • H. Reiju Mihara

    (Kagawa University)

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://econwpa.repec.org/eps/game/papers/0310/0310006.pdf
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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
Contact details of provider: Web page: http://econwpa.repec.org

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  1. 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.
  2. 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.
  3. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM.
  4. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
  5. H. Reiju Mihara, 1994. "Anonymity and Neutrality in Arrow's Theorem with Restricted Coalition Algebras," Public Economics 9411001, EconWPA, revised 22 Nov 1994.
  6. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
  7. 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.
  8. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997.
  9. 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.
  10. Mihara, H.R., 1994. "Arrow's Theorem and Turing Computability," Papers 276, Minnesota - Center for Economic Research.
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