  More than 100,000 children in the US foster care system are currently waiting
for an adoptive placement. Adoption agencies differ significantly in what
systems they use to identify matches between families and children. We consider
two prominent alternatives: (1) family-driven search, where families respond to
announcements made by the caseworker responsible for a child, and (2)
caseworker-driven search, where caseworkers utilize a software tool to perform
a targeted search for families. In this work, we compare these two systems via
a game-theoretic analysis. We introduce a dynamic search-and-matching model
that captures the heterogeneous preferences of families and children. This
allows us to study their incentives during the search process, and we can
compare the resulting welfare of the two systems in equilibrium. We first show
that, in general, no system dominates the other, neither in terms of family
welfare nor in terms of child welfare. This result maybe surprising, given that
the caseworker-driven approach employs a less wasteful search process. However,
we do identify various advantages of the caseworker-driven approach. Our main
theoretical result establishes that the equilibrium outcomes in
caseworker-driven search can Pareto-dominate the outcomes in family-driven
search, but not the other way around. We illustrate our results numerically to
demonstrate the effect different model parameters (e.g., search costs and
discount factors) have on welfare.
