Advanced Search
MyIDEAS: Login to save this paper or follow this series

Computability of simple games: A characterization and application to the core

Contents:

Author Info

  • Kumabe, Masahiro
  • Mihara, H. Reiju

Abstract

It was shown earlier that the class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games, strengthens the earlier result that computable games violate anonymity, and gives examples showing that the above inclusions are strict. It also extends Nakamura’s theorem about the nonemptyness of the core and shows that computable simple games have a finite Nakamura number, implying that the number of alternatives that the players can deal with rationally is restricted.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. 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/437/
File Function: original version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/3296/
File Function: revised version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/4403/
File Function: revised version
Download Restriction: no

File URL: http://mpra.ub.uni-muenchen.de/6803/
File Function: revised version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 437.

as in new window
Length:
Date of creation: Jul 2006
Date of revision:
Handle: RePEc:pra:mprapa:437

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

Related research

Keywords: Voting games; infinitely many players; recursion theory; Turingcomputability; computable manuals and contracts;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, Springer, vol. 10(2), pages 257-276.
  2. Itzhak Gilboa, 1990. "Philosophical Applications of Kolmogorov's Complexity Measure," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 923, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Truchon M., 1996. "Voting games and acyclic collective choice rules," Mathematical Social Sciences, Elsevier, Elsevier, vol. 31(1), pages 55-55, February.
  4. Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 59(4), pages S385-99, October.
  5. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521074650.
  6. H. Reiju Mihara, 2001. "Existence of a coalitionally strategyproof social choice function: A constructive proof," Social Choice and Welfare, Springer, Springer, vol. 18(3), pages 543-553.
  7. 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.
  8. Barton L. Lipman, 1995. "Information Processing and Bounded Rationality: A Survey," Canadian Journal of Economics, Canadian Economics Association, Canadian Economics Association, vol. 28(1), pages 42-67, February.
  9. Ariel Rubinstein, 1997. "Modeling Bounded Rationality," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262681005, December.
  10. Jonathan P. Thomas & Robert Evans, 2000. "Cooperation and Punishment," Game Theory and Information, EconWPA 0004002, EconWPA.
  11. Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer, Springer, vol. 23(2), pages 275-293, October.
  12. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(6), pages 943-953, June.
  13. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers, Centro de Investigacion Economica, ITAM 0211, Centro de Investigacion Economica, ITAM.
  14. Weber, Robert J., 1994. "Games in coalitional form," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 36, pages 1285-1303 Elsevier.
  15. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Computability of simple games: A complete investigation of the sixty-four possibilities," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 150-158, March.
  16. Andjiga, Nicolas Gabriel & Mbih, Boniface, 2000. "A note on the core of voting games," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 367-372, April.
  17. Mihara, H. Reiju, 2004. "Nonanonymity and sensitivity of computable simple games," Mathematical Social Sciences, Elsevier, Elsevier, vol. 48(3), pages 329-341, November.
  18. 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.
  19. Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003. "Social Choice and Electoral Competition in the General Spatial Model," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 188, Institut d'Économie Industrielle (IDEI), Toulouse.
  20. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
  21. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "The Nakamura numbers for computable simple games," MPRA Paper 3684, University Library of Munich, Germany.
  22. Anderlini, L. & Felli, L., 1993. "Incomplete Written Contracts: Undescribable States of Nature," Papers, Cambridge - Risk, Information & Quantity Signals 183, Cambridge - Risk, Information & Quantity Signals.
  23. 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, Springer, vol. 31(1), pages 39-45.
  24. Kam-Chau Wong & Marcel K. Richter, 1999. "Non-computability of competitive equilibrium," Economic Theory, Springer, Springer, vol. 14(1), pages 1-27.
  25. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  26. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 65, pages 135.
  27. Canning, David, 1992. "Rationality, Computability, and Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 60(4), pages 877-88, July.
  28. Anderlini, L. & Sabourian, H., 1991. "Cooperation and Effective Computability," Papers, Cambridge - Risk, Information & Quantity Signals 167, Cambridge - Risk, Information & Quantity Signals.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," MPRA Paper 11728, University Library of Munich, Germany.
  2. 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.
  3. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Computability of simple games: A complete investigation of the sixty-four possibilities," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 150-158, March.
  4. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "The Nakamura numbers for computable simple games," MPRA Paper 3684, University Library of Munich, Germany.

Lists

This item is featured on the following reading lists or Wikipedia pages:
  1. الگو:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Persian ne '')
  2. Template:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Japanese ne '')
  3. Txantiloi:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Basque ne '')
  4. قالب:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Arabic ne '')
  5. ライスの定理 in Wikipedia Japanese ne '')
  6. Rice's theorem in Wikipedia English ne '')
  7. User:Theorist2/Unused stuffs in Wikipedia English ne '')
  8. Template:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia English ne '')

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:437. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.