Cross-Sectional Dynamics in a Two-Sided Matching Model

This paper studies a dynamic search-theoretic model of two-sided
matching with ex ante heterogeneous agents and nontransferable utility.
There is a continuum of agents’ types in (0, 1), with both parties to the
match (x, y) receiving flow output xy. Foregone wages are the only cost
of search, and all productive relationships are mutual ‘tenant-at-will’.
Despite a continuum of distinct intertwined dynamic optimizations,
I characterize the search equilibrium starting with everyone unmatched:
There is a growing pool of permanently employed on [θt, 1), and an
elaborate web of temporary matches amongst lower types on (0, θt),
where θt ↓ 0. Thus, anyone is eventually is unwilling to accept a temporary
match. I develop an equilibrium concept addressing credibility
constraints, but argue that no matches are lost due to the absence of
binding contracts. I relate this to dynamic properties of flow values
that imply that no one ever quits a match more than once in his life.

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