A NEW NECESSARY CONDITION FOR NASH IMPLEMENTATION

In this paper we formulate a family of conditions called 'B-k-monotoni city' that are necessary for Nash implementation, where k is a natural number that indexes a particular condition, and where the condition o nly becomes more restrictive as k increases. B-k-monotonicity is in ge neral a stricter condition than Maskin monotonicity, and can be used t o show that certain social choice correspondences that satisfy Maskin monotonicity cannot be Nash implemented. (C) 1998 Elsevier Science S.A .