Representation of Effectivity Functions in Coalition Proof Nash Equilibrium: A Complete Characterization
AbstractThe concept of coalition proof Nash equilibrium was introduced by Bernheim, Peleg, and Whinston . 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 InfoPaper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 99-21.
Length: 23 pages
Date of creation: Mar 1999
Date of revision:
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effectivity functions; representation; coalition proof; Nash equilibrium;
Other versions of this item:
- 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.
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-03-04 (All new papers)
- NEP-CDM-2002-03-04 (Collective Decision-Making)
- NEP-GTH-2002-03-04 (Game Theory)
- NEP-MIC-2002-03-04 (Microeconomics)
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- Hans Keiding & Bezalel Peleg, 2004.
"Binary Effectivity Rules,"
Discussion Paper Series
dp378, 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 Paper Series dp324, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- 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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