Title: Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning

Abstract:

While federated learning (FL) traditionally relies on a central server to distribute training workloads, a market-driven approach allows clients to independently determine their training contributions based on rational self-interest. To analyze this dynamic, we introduce a potential game framework where a client’s payoff is a function of its specific effort and the incentives granted by the server. These incentives are shaped by the aggregate efforts of all participants and can be adjusted via a reward factor. Our analysis first confirms the existence of Nash equilibria (NEs) and subsequently examines their uniqueness within a stationary context. We demonstrate that NEs exhibit a nonlinear dependence on the reward factor, characterized by a nonsmooth transition at a critical threshold. At this point, the stationary potential loses its strict curvature, resulting in multiple NEs and a discontinuous shift between low-effort and high-effort strategies. Additionally, we establish the convergence of the best-response algorithm for computing these equilibria in our FL game. Finally, by applying the rational efforts derived from the NEs to FL training across various datasets and models, we validate the practical significance of the identified critical reward factor.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC