Your Recourse, My Loss? Algorithmic Recourse under Shared Constraints

Decision makers are increasingly relying on machine learning in sensitive situations. Algorithmic recourse aims to provide individuals with actionable and minimally costly steps to reverse unfavorable AI-driven decisions. While existing research focuses on single-individual (i.e., seeker) and single-model (i.e., provider) scenarios, real-world applications involve multiple stakeholders. Optimizing outcomes for seekers under an individual welfare approach overlooks the multi-agent nature of real-world systems, with competition for limited resources. Accordingly, we extend algorithmic recourse to a many-to-many setting with capacity constraints, where individually computed recourse recommendations no longer compose independently and stakeholder interactions affect recourse validity. We model this multi-agent algorithimc recourse as a capacitated weighted bipartite matching problem, based on recourse cost and provider capacity. Edge weights, reflecting recourse costs, are optimized for social welfare while quantifying the welfare gap between individual welfare and this collectively feasible outcome. We propose three optimization layers: capacitated matching, optimal capacity redistribution, and cost-aware optimization. We further model inequality-averse objectives through a concave social-welfare formulation that prioritizes the most disadvantaged seekers. Experiments demonstrate that our framework enables the many-to-many algorithmic recourse to achieve near-optimal welfare with minimum modification in system settings. Our results also show how recourse systems can be designed to balance aggregate welfare with distributive considerations. We extend algorithmic recourse from individual recommendations to system-level design, providing a tractable path toward higher social welfare while maintaining individual actionability.