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Heterogeneous buyers and sellers must make investments before entering a continuum assignment market. I show that efficient ex post contracting equilibria (Cole, Mailath, and Postlewaite 2001b) exist in a general assignment game framework. I then shed light on what enables and what precludes coordination failures. A simple condition—absence of technological multiplicity—guarantees efficient investments for each pair, but a mismatch of agents may still occur. However, using optimal transport theory, I also show that mismatch is heavily constrained in certain multidimensional environments with differentiated agents and no technological multiplicity. Under technological multiplicity, even extreme ex ante heterogeneity need not preclude inefficiencies. (JEL C78, D41, D86)