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Representation of Effectivity Functions in Coalition Proof Nash Equilibrium: A Complete Characterization

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Author Info
Hans Keiding (Institute of Economics, University of Copenhagen)
Bezalel Peleg (Hebrew University of Jerusalem)

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Abstract

The concept of coalition proof Nash equilibrium was introduced by Bernheim, Peleg, and Whinston [1987]. 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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Publisher Info
Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 99-21.

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Length: 23 pages
Date of creation: Mar 1999
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Handle: RePEc:kud:kuiedp:9921

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Related research
Keywords: effectivity functions; representation; coalition proof; Nash equilibrium;

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Find related papers by JEL classification:
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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  1. Hans Keiding & Bezalel Peleg, 2004. "Binary Effectivity Rules," Discussion Paper Series dp378, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
    Other versions:
  2. Hans Keiding & Bezalel Peleg, 2003. "On the Continuity of Representations of Effectivity Functions," Discussion Paper Series dp324, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
    Other versions:
  3. Bezalel Peleg, 2002. "Complete Characterization of Acceptable Game Forms by Effectivity Functions," Discussion Paper Series dp283, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  4. Daniel Seidmann, 2006. "Perverse Committee Appointments May Foster Divide and Rule," Discussion Papers 2006-08, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham. [Downloadable!]
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