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

Authors: 
Hans Keiding & Bezalel Peleg
Abstract: 

The 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.

Date: 
August, 2000
Published in: 
Social Choice and Welfare 19 (2002), 241-263
Number: 
223