Abstract:

We consider the problem of implementing a social choice correspondence H in Nash equilibrium when the constitution of the society is given by an effectivity function E. It is assumed that the effectivity function of H, E^H, is a sub-correspondence of E. We found necessary and efficient conditions for a game form Gamma to implement H (in Nash equilibria) and to satisfy, at the same time, that E^Gamma, the effectivity function of Gamma, is a sub-correspondence of E^H (which guarantees that Gamma is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of E^Gamma and E^H, and for E^Gamma=E^H. All our results are sharp as is shown by suitable examples.

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