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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.

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

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Date of creation: Jul 2006
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Handle: RePEc:pra:mprapa:437
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  1. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650.
  2. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276.
  3. Truchon, M., 1993. "Voting Games and Acyclic Collective Choice Rules," Papers 9315, Laval - Recherche en Politique Economique.
  4. Canning, David, 1992. "Rationality, Computability, and Nash Equilibrium," Econometrica, Econometric Society, vol. 60(4), pages 877-88, July.
  5. H. Reiju Mihara, 2001. "Existence of a coalitionally strategyproof social choice function: A constructive proof," Social Choice and Welfare, Springer, vol. 18(3), pages 543-553.
  6. Luca Anderlini & Leonardo Felli, 1994. "Incomplete Written Contracts: Undescribable States of Nature," The Quarterly Journal of Economics, Oxford University Press, vol. 109(4), pages 1085-1124.
  7. 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.
  8. Ariel Rubinstein, 2005. "Modeling Bounded Rationality," Levine's Bibliography 784828000000000152, UCLA Department of Economics.
  9. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
  10. Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003. "Social Choice and Electoral Competition in the General Spatial Model," IDEI Working Papers 188, Institut d'Économie Industrielle (IDEI), Toulouse.
  11. Barton L. Lipman, 1995. "Information Processing and Bounded Rationality: A Survey," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 42-67, February.
  12. Andrei Gomberg & César Martinelli & Ricard Torres, 2005. "Anonymity in large societies," Social Choice and Welfare, Springer, vol. 25(1), pages 187-205, October.
  13. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
  14. 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.
  15. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  16. 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.
  17. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June.
  18. Kam-Chau Wong & Marcel K. Richter, 1999. "Non-computability of competitive equilibrium," Economic Theory, Springer, vol. 14(1), pages 1-27.
  19. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004.
  20. Itzhak Gilboa, 1990. "Philosophical Applications of Kolmogorov's Complexity Measure," Discussion Papers 923, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. 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.
  22. 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.
  23. Anderlini, Luca & Sabourian, Hamid, 1995. "Cooperation and Effective Computability," Econometrica, Econometric Society, vol. 63(6), pages 1337-69, November.
  24. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "The Nakamura numbers for computable simple games," MPRA Paper 3684, University Library of Munich, Germany.
  25. Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer, vol. 23(2), pages 275-293, October.
  26. 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.
  27. Evans, Robert & Thomas, Jonathan P, 2001. "Cooperation and Punishment," Econometrica, Econometric Society, vol. 69(4), pages 1061-75, July.
  28. 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.
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