Constitutional implementation

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 , is a sub-correspondence of E. We found necessary and efficient conditions for a game form to implement H (in Nash equilibria), and to satisfy, at the same time, that , the effectivity function of , is a sub-correspondence of (which guarantees that is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of and , and for . All our results are sharp as is shown by suitable examples. Received: 15 December 2000 / Accepted: 3 September 2001