Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization
The concept of coalition proof Nash equilibrium was introduced by Bernheim et al. . 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.
Volume (Year): 19 (2002)
Issue (Month): 2 ()
|Note:||Received: 24 June 1999/Accepted: 20 September 2000|
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