On the Continuity of Representations of Effectivity Functions
AbstractAn 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 InfoPaper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 03-30.
Length: 19 pages
Date of creation: May 2003
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Other versions of this item:
- Keiding, Hans & Peleg, Bezalel, 2006. "On the continuity of representations of effectivity functions," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 827-842, November.
- Hans Keiding & Bezalel Peleg, 2003. "On the Continuity of Representations of Effectivity Functions," Discussion Paper Series dp324, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- 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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- 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.
- Hans Keiding & Bezalel Peleg, 1999. "Representation of Effectivity Functions in Coalition Proof Nash Equilibrium: A Complete Characterization," Discussion Papers 99-21, University of Copenhagen. Department of Economics.
- Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
- Hans Keiding & Bezalel Peleg, 1999.
"Stable Voting Procedures for Committees in Economic Environments,"
99-20, University of Copenhagen. Department of Economics.
- 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.
- Amartya Sen, 1999. "The Possibility of Social Choice," American Economic Review, American Economic Association, vol. 89(3), pages 349-378, June.
- Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 139-157, October.
- 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.
- Holzman, Ron, 1986. "On strong representations of games by social choice functions," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 39-57, February.
- Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
- 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," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) hal-00666816, HAL.
- 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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