From Individual to Multi-Agent Algorithmic Recourse: Minimizing the Welfare Gap via Capacitated Bipartite Matching

Zahra Khotanlou, Kate Larson, Amir-Hossein Karimi

Keywords: Algorithmic Recourse, Multi-Agent Systems, Social Welfare Optimization, Bipartite Matching

Abstract: Decision makers are increasingly relying on machine learning in sensitive situations. In such settings, algorithmic recourse aims to provide individuals with actionable and minimally costly steps to reverse unfavorable AI-driven decisions. While existing research predominantly focuses on single-individual (i.e., seeker) and single-model (i.e., provider) scenarios, real-world applications often involve multiple interacting stakeholders. Optimizing outcomes for seekers under an individual welfare approach overlooks the inherently multi-agent nature of real-world systems, where individuals interact and compete for limited resources. To address this, we introduce a novel framework for multi-agent algorithmic recourse that accounts for multiple recourse seekers and recourse providers. We model this many-to-many interaction as a capacitated weighted bipartite matching problem, where matches are guided by both recourse cost and provider capacity. We propose a three-layer optimization framework: (1) basic capacitated matching, (2) optimal capacity redistribution to minimize the welfare gap, and (3) cost-aware optimization balancing welfare maximization with capacity adjustment costs. Experimental validation demonstrates that our framework enables near-optimal welfare with minimal system modifications.

Submission Number: 18