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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, Studiestraede 6, 1455 Copenhagen K., Denmark)
Bezalel Peleg (Institute of Mathematics and Center for Rationality and Interactive Decision Theory, Hebrew University of Jerusalem)

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Abstract

The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. [5]. 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
Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 19 (2002)
Issue (Month): 2 ()
Pages: 241-263
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Handle: RePEc:spr:sochwe:v:19:y:2002:i:2:p:241-263

Note: Received: 24 June 1999/Accepted: 20 September 2000
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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. 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!]
  3. Hans Keiding & Bezalel Peleg, 2003. "On the Continuity of Representations of Effectivity Functions," Discussion Papers 03-30, University of Copenhagen. Department of Economics. [Downloadable!]
    Other versions:
  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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