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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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Web page: http://www.elsevier.com/locate/jmateco

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  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. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  3. Anderlini, L. & Sabourian, H., 1991. "Cooperation and Effective Computability," Papers 167, Cambridge - Risk, Information & Quantity Signals.
  4. Andrei Gomberg & César Martinelli & Ricard Torres, 2005. "Anonymity in large societies," Social Choice and Welfare, Springer, vol. 25(1), pages 187-205, October.
  5. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
  6. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
  7. 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.
  8. 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.
  9. 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.
  10. Truchon M., 1996. "Voting games and acyclic collective choice rules," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 55-55, February.
  11. H. Reiju Mihara, 1994. "Arrow's Theorem and Turing Computability," Public Economics 9408001, EconWPA, revised 23 Aug 1994.
  12. Anderlini, L. & Felli, L., 1993. "Incomplete Written Contracts: Undescribable States of Nature," Papers 183, Cambridge - Risk, Information & Quantity Signals.
  13. 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.
  14. Mihara, H. Reiju, 2004. "Nonanonymity and sensitivity of computable simple games," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 329-341, November.
  15. 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.
  16. Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer, vol. 23(2), pages 275-293, October.
  17. H. Reiju Mihara, 1996. "Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof," Public Economics 9604002, EconWPA, revised 20 Sep 1996.
  18. 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.
  19. Jonathan P. Thomas & Robert Evans, 2000. "Cooperation and Punishment," Game Theory and Information 0004002, EconWPA.
  20. Ariel Rubinstein, 2005. "Modeling Bounded Rationality," Levine's Bibliography 784828000000000152, UCLA Department of Economics.
  21. Canning, David, 1992. "Rationality, Computability, and Nash Equilibrium," Econometrica, Econometric Society, vol. 60(4), pages 877-88, July.
  22. 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.
  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. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June.
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Cited by:
  1. 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.
  2. 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.
  3. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," Games and Economic Behavior, Elsevier, vol. 72(1), pages 187-201, May.
  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.

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