Two-Sided Investment and Matching with Multidimensional Cost Types and Attributes

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.