Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization

Hans Keiding () and Bezalel Peleg
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Hans Keiding: Institute of Economics, University of Copenhagen, Studiestraede 6, 1455 Copenhagen K., Denmark

Social Choice and Welfare, 2002, vol. 19, issue 2, 263 pages

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.

Date: 2002-04-10
Note: Received: 24 June 1999/Accepted: 20 September 2000
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Working Paper: Representation of Effectivity Functions in Coalition Proof Nash Equilibrium: A Complete Characterization (1999)
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