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On the Continuity of Representations of Effectivity Functions

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  • Hans Keiding

    (University of Copenhagen, Institute of Economics)

  • Bezalel Peleg

    (Hebrew University of Jerusalem)

Abstract

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that speci?ed by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 03-30.

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Length: 19 pages
Date of creation: May 2003
Date of revision:
Handle: RePEc:kud:kuiedp:0330

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  1. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, Elsevier, vol. 43(2), pages 267-287, March.
  2. Holzman, Ron, 1986. "On strong representations of games by social choice functions," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 39-57, February.
  3. Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine 123456789/13220, Paris Dauphine University.
  4. Hans Keiding & Bezalel Peleg, 1999. "Stable Voting Procedures for Committees in Economic Environments," Discussion Papers 99-20, University of Copenhagen. Department of Economics.
  5. Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, Elsevier, vol. 12(2), pages 139-157, October.
  6. Amartya Sen, 1999. "The Possibility of Social Choice," American Economic Review, American Economic Association, American Economic Association, vol. 89(3), pages 349-378, June.
  7. Hans Keiding & Bezalel Peleg, 2002. "Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization," Social Choice and Welfare, Springer, Springer, vol. 19(2), pages 241-263, April.
  8. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, Springer, vol. 15(1), pages 67-80.
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Cited by:
  1. Agnieszka Rusinowska, 2013. "Book review on "Bezalel Peleg and Hans Peters: Strategic Social Choice. Stable Representations of Constitutions", Studies in choice and welfare, Springer, 2010, 154 pp," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00666816, HAL.
  2. Agnieszka Rusinowska, 2013. "Bezalel Peleg and Hans Peters: Strategic social choice. Stable representations of constitutions," Social Choice and Welfare, Springer, Springer, vol. 40(2), pages 631-634, February.

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