Toward a Sustainable Federated Learning Ecosystem: A Practical Least Core Mechanism for Payoff Allocation

Emerging network paradigms and applications increasingly rely on federated learning (FL) to enable collaborative intelligence while preserving privacy. However, the sustainability of such collaborative environments hinges on a fair and stable payoff allocation mechanism. Focusing on coalition stability, this paper introduces a payoff allocation framework based on the least core (LC) concept. Unlike traditional methods, the LC prioritizes the cohesion of the federation by minimizing the maximum dissatisfaction among all potential subgroups, ensuring that no participant has an incentive to break away. To adapt this game-theoretic concept to practical, large-scale networks, we propose a streamlined implementation with a stack-based pruning algorithm, effectively balancing computational efficiency with allocation precision. Case studies in federated intrusion detection demonstrate that our mechanism correctly identifies pivotal contributors and strategic alliances. The results confirm that the practical LC framework promotes stable collaboration and fosters a sustainable FL ecosystem.