Beauty is a Beast, Frog is a Prince: Assortative Matching with Nontransferabilities

We present sufficient conditions for monotone matching in environments where utility is not fully transferable between partners. These conditions involve complementarity in types not only of the total payoff to a match, as in the transferable utility case, but also in the degree of transferability between partners. We apply our conditions to study some models of risk sharing and incentive problems, deriving new results for predicted matching patterns in those contexts