Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization
AbstractThe concept of coalition proof Nash equilibrium was introduced by Bernheim et al. . In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium. It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function.
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Bibliographic InfoArticle provided by Springer in its journal Social Choice and Welfare.
Volume (Year): 19 (2002)
Issue (Month): 2 ()
Note: Received: 24 June 1999/Accepted: 20 September 2000
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Other versions of this item:
- 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.
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- Hans Keiding & Bezalel Peleg, 2006.
"Binary effectivity rules,"
Review of Economic Design,
Springer, vol. 10(3), pages 167-181, December.
- 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.
- 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 Papers 03-30, University of Copenhagen. Department of Economics.
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