Federated learning (FL) enables collaborative model training without directly sharing data, thereby offering effective privacy guarantees. However, the decentralized architecture of FL makes it vulnerable to backdoor attacks, where adversaries can compromise a subset of clients to inject malicious updates, causing the global model to misbehave on specific trigger inputs. The existing defenses typically rely on static rules or auxiliary validation data, which often lack adaptability against evolving attack strategies or introduce privacy risks and computational overhead. To address these challenges, we propose GameRLFed, a robust defense framework that formulates the FL security problem as a repeated game with incomplete information. Without requiring any auxiliary data, the server infers the malicious tendencies of each client based on current updates and historical observations and employs reinforcement learning to dynamically adjust the aggregation weights for mitigating backdoor effects. Moreover, attackers adaptively evolve their strategies in response to the behavior of the server to maximize the effectiveness of their attacks while minimizing the risk of detection, resulting in complex game interactions. Theoretically, we prove that GameRLFed can converge to a near-optimal global model under adversarial dynamics. Extensive experiments conducted across multiple datasets and attack types show that GameRLFed outperforms six baseline methods in terms of robustness, adaptability, and computational efficiency.
