CFDP Revision Date
We study markets in which agents ﬁrst make investments and are then matched into potentially productive partnerships. Equilibrium investments and the equilibrium matching will be eﬀicient if agents can simultaneously negotiate investments and matches, but we focus on markets in which agents must ﬁrst sink their investments before matching. Additional equilibria may arise in this sunk-investment setting, even though our matching market is competitive. These equilibria exhibit ineﬀiciencies that we can interpret as coordination failures. All allocations satisfying a constrained eﬀiciency property are equilibria, and the converse holds if preferences satisfy a separability condition. We identify suﬀicient conditions (most notably, quasiconcave utilities) for the investments of matched agents to satisfy an exchange eﬀiciency property as well as suﬀicient conditions (most notably, a single crossing property) for agents to be matched positive assortatively, with these conditions then forming the core of suﬀicient conditions for the eﬀiciency of equilibrium allocations.
Nöldeke, Georg and Samuelson, Larry, "Investment and Competitive Matching" (2014). Cowles Foundation Discussion Papers. 2347.