  To find families for the more than 100,000 children in need of adoptive
placements, most United States child welfare agencies have employed a
family-driven search strategy in which prospective families respond to
announcements made by the agency. However, some agencies have switched to a
caseworker-driven search strategy in which the caseworker directly contacts
families recommended for a child. We introduce a novel search-and-matching
model to capture essential aspects of the adoption process and compare the two
approaches through a game-theoretical analysis. We show that the search
equilibria induced by threshold strategies form a lattice structure under
either approach. Our main theoretical result establishes that the equilibrium
outcomes in family-driven search can never Pareto dominate the outcomes in
caseworker-driven search, but it is possible that each caseworker-driven search
outcome Pareto dominates all family-driven search outcomes. We also find that
when families are sufficiently impatient, caseworker-driven search is better
for all children. We illustrate numerically that most agents are better off
under caseworker-driven search for a wide range of parameters. Finally, we
provide empirical evidence from an agency that switched to caseworker-driven
search and achieved a three-year adoption probability that outperformed a
statewide benchmark by 17%.
