🤖 AI Summary
This paper addresses inefficiency and inequity in matching over 100,000 children awaiting adoption in the U.S. foster care system. Method: We develop a game-theoretic adoption matching model to systematically compare two search paradigms—family-initiated (demand-driven) versus caseworker-initiated (supply-driven) matching—and integrate equilibrium analysis, large-scale numerical simulation, and causal inference via policy-switching experiments. Contribution/Results: We introduce the novel concept of threshold-strategy equilibrium lattice structure, rigorously proving that caseworker-driven matching Pareto-dominates family-driven matching under mild conditions—crucially contingent on “family impatience” as the key determinant. Empirically, the caseworker-driven strategy increases three-year adoption rates by 17% relative to state benchmarks; simulations confirm consistent utility gains for all participants across most parameter regimes. This work establishes the first theoretically rigorous and empirically validated matching framework for public child welfare systems.
📝 Abstract
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%.
