Monotone matching in perfect and imperfect worlds

We study frictionless matching models in large production economies with and without market imperfections and/or incentive problems. We provide necessary and sufficient distribution-free conditions for monotone matching which depend on the relationship between what we call the segregation payoff --- a generalization of the individually rational payoff --- and the feasible set for a pair of types. Our approach yields some new techniques for computing equilibria, particularly when utility is not transferable. It also helps to underscore the effects of imperfections, which have two distinct effects that are relevant for equilibrium matching patterns: they can overwhelm the complementarity properties of the production technology and they can introduce nontransferabilities that make equilibrium matching inefficient. We also use our framework to reveal the source of differences in the comparative static properties of some models in the literature and to explore the effects of distribution on the equilibrium matching pattern.