Nash Implementation of Stable Solutions in Many-to-One Matching Problems : The Case with No Complementarities

We study Nash implementation in many-to-one matching problems also known as college admission problems [Gale and Shapley, College admission and the stability of marriage, Amer. Math. Monthly 69 (1962) 9-15]. In contrast to the previous literature we make no assumptions regarding the preference domain beyond responsiveness [Roth, The college admissions problem is not equivalent to the marriage problem, J. Econ. Theory 36 (1985) 277-288] which rules out complementarities. We show that although subsolutions of the stable many-to-one matching rule do not in general satisfy no veto power, monotonicity is not only a necessary condition, but a suffcient one as well