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

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  • 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.

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Bibliographic Info

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

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

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Handle: RePEc:eee:mateco:v:44:y:2008:i:3-4:p:348-366

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  1. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(3-4), pages 348-366, February.
  2. Canning, David, 1992. "Rationality, Computability, and Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 60(4), pages 877-88, July.
  3. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(6), pages 943-953, June.
  4. Ariel Rubinstein, 2005. "Modeling Bounded Rationality," Levine's Bibliography 784828000000000152, UCLA Department of Economics.
  5. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 32(3), pages 339-354, November.
  6. 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.
  7. Evans, Robert & Thomas, Jonathan P, 2001. "Cooperation and Punishment," Econometrica, Econometric Society, Econometric Society, vol. 69(4), pages 1061-75, July.
  8. Masahiro Kumabe & H. Reiju Mihara, 2008. "The Nakamura numbers for computable simple games," Social Choice and Welfare, Springer, Springer, vol. 31(4), pages 621-640, December.
  9. 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.
  10. Truchon, Michel, 1995. "Voting games and acyclic collective choice rules," Mathematical Social Sciences, Elsevier, Elsevier, vol. 29(2), pages 165-179, April.
  11. Anderlini, L. & Sabourian, H., 1991. "Cooperation and Effective Computability," Papers, Cambridge - Risk, Information & Quantity Signals 167, Cambridge - Risk, Information & Quantity Signals.
  12. Andjiga, Nicolas Gabriel & Mbih, Boniface, 2000. "A note on the core of voting games," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 33(3), pages 367-372, April.
  13. 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.
  14. 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.
  15. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information, EconWPA 0310006, EconWPA, revised 01 Jun 2004.
  16. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, Springer, vol. 10(2), pages 257-276.
  17. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 17(1), pages 1-8, February.
  18. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany.
  19. Kam-Chau Wong & Marcel K. Richter, 1999. "Non-computability of competitive equilibrium," Economic Theory, Springer, Springer, vol. 14(1), pages 1-27.
  20. 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.
  21. Anderlini, Luca & Felli, Leonardo, 1994. "Incomplete Written Contracts: Undescribable States of Nature," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 109(4), pages 1085-1124, November.
  22. Peleg, Bezalel, 2002. "Game-theoretic analysis of voting in committees," Handbook of Social Choice and Welfare, Elsevier, 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.
  23. H. Reiju Mihara, 1996. "Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof," Public Economics, EconWPA 9604002, EconWPA, revised 20 Sep 1996.
  24. Andrei Gomberg & César Martinelli & Ricard Torres, 2005. "Anonymity in large societies," Social Choice and Welfare, Springer, Springer, vol. 25(1), pages 187-205, October.
  25. Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer, Springer, vol. 23(2), pages 275-293, October.
  26. 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.
  27. Armstrong, Thomas E., 1985. "Precisely dictatorial social welfare functions : Erratum and Addendum to `arrows theorem with restricted coalition algebras'," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 14(1), pages 57-59, February.
  28. 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.
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Citations

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Cited by:
  1. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," Games and Economic Behavior, Elsevier, Elsevier, vol. 72(1), pages 187-201, May.
  2. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(3-4), pages 348-366, February.
  3. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "The Nakamura numbers for computable simple games," MPRA Paper 3684, University Library of Munich, Germany.
  4. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany.

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