We present sufficient conditions for monotone matching in environments where utility is not fully transferable between partners. These conditions involve not only complementarity in types of the total payoff to a match, as in the transferable utility case, but also monotonicity in type of the...

Mobility depends essentially on investment, which often occurs in environments in which individuals match (school) or will match after investing (the labor market). Where partners can transfer surplus to each other only imperfectly (NTU), the pattern of matching will typically be inefficient,...