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On the continuity of representations of effectivity functions

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  • Keiding, Hans
  • Peleg, Bezalel

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 ?nd 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

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

Volume (Year): 42 (2006)
Issue (Month): 7-8 (November)
Pages: 827-842

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Handle: RePEc:eee:mateco:v:42:y:2006:i:7-8:p:827-842

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  1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
  2. Hans Keiding & Bezalel Peleg, 2002. "Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization," Social Choice and Welfare, Springer, vol. 19(2), pages 241-263.
  3. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  4. Keiding, Hans & Peleg, Bezalel, 2001. "Stable voting procedures for committees in economic environments," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 117-140, November.
  5. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
  6. Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 139-157, October.
  7. Amartya Sen, 1999. "The Possibility of Social Choice," American Economic Review, American Economic Association, vol. 89(3), pages 349-378, June.
  8. Holzman, Ron, 1986. "On strong representations of games by social choice functions," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 39-57, February.
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Cited by:
  1. repec:hal:cesptp:hal-00666816 is not listed on IDEAS
  2. Agnieszka Rusinowska, 2013. "Bezalel Peleg and Hans Peters: Strategic social choice. Stable representations of constitutions," Social Choice and Welfare, Springer, vol. 40(2), pages 631-634, February.

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