Equity Implications of Federal-Local Cost-Sharing in Flood Buyouts: A Game-Theoretic Analysis with Heterogeneous Homeowners

Climate-driven flood risk increasingly necessitates managed retreat through government buyout programmes, yet empirical evidence documents substantial racial and economic disparities in programme implementation. Here we develop a three-level Stackelberg game to analyse how federal-local cost-sharing arrangements generate inequitable outcomes through strategic interactions among federal authorities, local governments, and heterogeneous homeowners. Our model reveals three distinct mechanisms driving inequity: differential discount rates across income groups, local governments' tax-base preservation incentives, and participation thresholds that exclude fiscally constrained communities. Numerical analysis of 34,493 households across nine flood-prone US regions demonstrates that the current Federal Emergency Management Agency 75/25 cost-sharing arrangement produces a relocation ratio gap of 0.26--low-income households relocate at roughly one-quarter the rate of high-income households. Achieving near-equity requires federal cost shares of at least 85%, though equity-weighted mechanisms can attain similar outcomes at 25% lower cost. These findings provide a theoretical foundation for understanding observed disparities and identify policy levers for more equitable climate adaptation.