On the Continuity of Representations of Effectivity Functions
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.
|Date of creation:||May 2003|
|Contact details of provider:|| Postal: Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K., Denmark|
Phone: (+45) 35 32 30 10
Fax: +45 35 32 30 00
Web page: http://www.econ.ku.dk
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 139-157, October.
- Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
- 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.
- Hans Keiding & Bezalel Peleg, 1999. "Stable Voting Procedures for Committees in Economic Environments," Discussion Papers 99-20, University of Copenhagen. Department of Economics.
- Holzman, Ron, 1986. "On strong representations of games by social choice functions," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 39-57, February.
- 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.
- 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.
- 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.
- 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.
- repec:dau:papers:123456789/13220 is not listed on IDEAS
- Amartya Sen, 1999. "The Possibility of Social Choice," American Economic Review, American Economic Association, vol. 89(3), pages 349-378, June.
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:kud:kuiedp:0330. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Hoffmann)
If references are entirely missing, you can add them using this form.