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On the Continuity of Representations of Effectivity Functions

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  • Hans Keiding

    ()

  • Bezalel Peleg

    ()

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.

Suggested Citation

  • Hans Keiding & Bezalel Peleg, 2003. "On the Continuity of Representations of Effectivity Functions," Discussion Paper Series dp324, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp324
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    References listed on IDEAS

    as
    1. Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 139-157, October.
    2. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    3. 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.
    4. Holzman, Ron, 1986. "On strong representations of games by social choice functions," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 39-57, February.
    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. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 67-80.
    7. Hans Keiding & Bezalel Peleg, 2002. "Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 241-263.
    8. repec:dau:papers:123456789/13220 is not listed on IDEAS
    9. Amartya Sen, 1999. "The Possibility of Social Choice," American Economic Review, American Economic Association, vol. 89(3), pages 349-378, June.
    10. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
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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;The Society for Social Choice and Welfare, vol. 40(2), pages 631-634, February.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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