Federated learning (FL) is an emerging paradigm for training machine learning models across distributed clients. Traditionally, in FL settings, a central server assigns training efforts (or strategies) to clients. However, from a market-oriented perspective, clients may independently choose their training efforts based on rational self-interest. To explore this, we propose a potential game framework where each client's payoff is determined by their individual efforts and the rewards provided by the server. The rewards are influenced by the collective efforts of all clients and can be modulated through a reward factor. Our study begins by establishing the existence of Nash equilibria (NEs), followed by an investigation of uniqueness in homogeneous settings. We demonstrate a significant improvement in clients' training efforts at a critical reward factor, identifying it as the optimal choice for the server. Furthermore, we prove the convergence of the best-response algorithm to compute NEs for our FL game. Finally, we apply the training efforts derived from specific NEs to a real-world FL scenario, validating the effectiveness of the identified optimal reward factor.

翻译：联邦学习（FL）是一种在分布式客户端上训练机器学习模型的新兴范式。传统上，在联邦学习设置中，中央服务器会向客户端分配训练努力（或策略）。然而，从市场导向的视角来看，客户端可能会基于理性的自利动机独立选择其训练努力。为探究此问题，我们提出了一个势博弈框架，其中每个客户端的收益由其个体努力以及服务器提供的奖励决定。奖励受到所有客户端集体努力的影响，并可通过一个奖励因子进行调节。我们的研究首先确立了纳什均衡（NEs）的存在性，随后探究了同质设置下的唯一性。我们证明了在某个临界奖励因子处，客户端的训练努力会得到显著提升，并将其识别为服务器的最优选择。此外，我们证明了最佳响应算法在计算此联邦学习博弈的纳什均衡时的收敛性。最后，我们将从特定纳什均衡推导出的训练努力应用于一个真实世界的联邦学习场景，验证了所识别的最优奖励因子的有效性。