I study settings in which heterogeneous buyers and sellers, characterized by cost
types, must invest in attributes before they compete for partners in a frictionless,
continuum assignment market. I define Cole, Mailath and Postlewaite's (2001a) notion
of ex-post contracting equilibrium in a general assignment game framework. Ex-ante efficient
investment and matching can always be supported in equilibrium.
The main part of the paper sheds light on what enables and what precludes
coordination failures resulting in mismatch of agents (from an ex-ante perspective)
and/or pairwise inefficient investments. A kind of technological multiplicity
is the key source of potential inefficiencies. Absence of technological multiplicity rules out
pairwise inefficient investments, and it heavily constrains mismatch in multi-dimensional environments with
differentiated agents. An example with simultaneous under- and over-investment shows that
even extreme exogenous heterogeneity may not suffice to rule out inefficient
equilibria in environments with technological multiplicity.