1. t(x ?)) hold for all x, x ? ? X. Similarly, letting R Y be the set of functions from Y to R, we may define (v, x) ? R Y � X Y to be implementable by an incentive compatible direct mechanism if there exists t ? R Y such that v(y) = ?(y, x(y), t(y)) and ?(y, x(y), t(y)) ? ?(y, x(y ?), t(y ?)) hold for all;Let R X be the set of functions from X to R. Then (u, y) ? , y(x), t(x)) and the incentive compatibility conditions ?(x, y(x), t(x)) ? ?(x, y(x ?)
2. On a Characterization of Stable Matchings;H Adachi;Economics Letters,2000