This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

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

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Kumabe, Masahiro
Mihara, H. Reiju

Additional information is available for the following registered author(s):

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.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help file. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://mpra.ub.uni-muenchen.de/440/
File Format:
File Function: orginal version
Download Restriction: no
File URL: http://mpra.ub.uni-muenchen.de/4405/
File Format:
File Function: revised version
Download Restriction: no

Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 440.

Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Length:
Date of creation: Aug 2007
Date of revision:
Handle: RePEc:pra:mprapa:440

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Ekkehart Schlicht).

Related research
Keywords: Voting games axiomatic method complete independence Turing computability legal precedents

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
C69 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Other

This paper has been announced in the following NEP Reports:

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. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276. [Downloadable!] (restricted)
    Other versions:
  2. Nabil I. Al-Najjar & Luca Anderlini & Leonardo Felli, 2003. "Undescribable Events," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
    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. Anderlini, L. & Felli, L., 1993. "Incomplete Written Contracts: Undescribable States of Nature," Papers 183, Cambridge - Risk, Information & Quantity Signals.
    Other versions:
  5. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November. [Downloadable!] (restricted)
  6. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004. [Downloadable!]
    Other versions:
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  12. 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. [Downloadable!] (restricted)
    Other versions:
Full references

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. "The Nakamura numbers for computable simple games," MPRA Paper 3684, University Library of Munich, Germany. [Downloadable!]
Statistics
Access and download statistics

Did you know? Apart from a small start up grant in the 1990's, RePEc has received no funding and lives on the help of volunteers.

This page was last updated on 2008-9-5.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.