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