Search and Matching for Adoption from Foster Care

More than 100,000 children in the foster care system are currently waiting for an adoptive placement in the United States, where adoptions from foster care occur through a semi-decentralized search and matching process with the help of local agencies. Traditionally, most agencies have employed a family-driven search process, where prospective families respond to announcements made by the caseworker responsible for a child. However, recently some agencies switched to a caseworker-driven search process, where the caseworker conducts a targeted search of suitable families for the child. We introduce a novel search-and-matching model to capture essential aspects of adoption and compare these two search processes through a game-theoretical analysis. We show that the search equilibria induced by (novel) 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 there are instances where 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 for a wide range of parameters, most agents are better off under caseworker-driven search.