IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

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

  • Kumabe, Masahiro
  • Mihara, H. Reiju

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.

(This abstract was borrowed from another version of this item.)

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://www.sciencedirect.com/science/article/B6VBY-4NX2NN6-3/2/cc48731f27a33a567fa46525be31b518
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 3-4 (February)
Pages: 348-366

as
in new window

Handle: RePEc:eee:mateco:v:44:y:2008:i:3-4:p:348-366
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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. 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.
  2. Anderlini, Luca & Sabourian, Hamid, 1995. "Cooperation and Effective Computability," Econometrica, Econometric Society, vol. 63(6), pages 1337-69, November.
  3. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
  4. 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.
  5. Mihara, H.R., 1994. "Arrow's Theorem and Turing Computability," Papers 276, Minnesota - Center for Economic Research.
  6. 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.
  7. H. Reiju Mihara, 1996. "Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof," Public Economics 9604002, EconWPA, revised 20 Sep 1996.
  8. 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.
  9. Anderlini, L. & Felli, L., 1993. "Incomplete Written Contracts: Undescribable States of Nature," Papers 183, Cambridge - Risk, Information & Quantity Signals.
  10. Jonathan P. Thomas & Robert Evans, 2000. "Cooperation and Punishment," Game Theory and Information 0004002, EconWPA.
  11. Barton L. Lipman, 1993. "Information Processing and Bounded Rationality: A Survey," Working Papers 872, Queen's University, Department of Economics.
  12. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004.
  13. 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.
  14. Ariel Rubinstein, 1997. "Modeling Bounded Rationality," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262681005, June.
  15. Itzhak Gilboa, 1990. "Philosophical Applications of Kolmogorov's Complexity Measure," Discussion Papers 923, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer, vol. 23(2), pages 275-293, October.
  17. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
  18. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  19. Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," The Journal of Business, University of Chicago Press, vol. 59(4), pages S385-99, October.
  20. 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.
  21. 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.
  22. Truchon, M., 1993. "Voting Games and Acyclic Collective Choice Rules," Papers 9315, Laval - Recherche en Politique Economique.
  23. Kam-Chau Wong & Marcel K. Richter, 1999. "Non-computability of competitive equilibrium," Economic Theory, Springer, vol. 14(1), pages 1-27.
  24. 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.
  25. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM.
  26. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June.
  27. 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.
  28. Canning, David, 1992. "Rationality, Computability, and Nash Equilibrium," Econometrica, Econometric Society, vol. 60(4), pages 877-88, July.
Full references (including those not matched with items on IDEAS)

This item is featured on the following reading lists or Wikipedia pages:

  1. ライスの定理 in Wikipedia Japanese ne '')
  2. الگو:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Persian ne '')
  3. User:Theorist2/Unused stuffs in Wikipedia English ne '')
  4. قالب:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Arabic ne '')
  5. Rice's theorem in Wikipedia English ne '')
  6. Txantiloi:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Basque ne '')
  7. Template:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia Japanese ne '')
  8. Template:Cite doi/10.1016.2Fj.jmateco.2007.05.012 in Wikipedia English ne '')

When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:44:y:2008:i:3-4:p:348-366. 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: (Zhang, Lei)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.