arXiv:2510.26841v1 Announce Type: cross Abstract: Federated Learning (FL) enables collaborative model training without data sharing, yet participants face a fundamental challenge, e.g., simultaneously ensuring fairness across demographic groups while protecting sensitive client data. We introduce a differentially private fair FL algorithm (\textit{FedPF}) that transforms this multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility. Our theoretical analysis reveals a surprising inverse relationship, i.e., stricter privacy protection fundamentally limits the system's ability to detect and correct demographic biases, creating an inherent tension between privacy and fairness. Counterintuitively, we prove that moderate fairness constraints initially improve model generalization before causing performance degradation, where a non-monotonic relationship that challenges conventional wisdom about fairness-utility tradeoffs. Experimental validation demonstrates up to 42.9 % discrimination reduction across three datasets while maintaining competitive accuracy, but more importantly, reveals that the privacy-fairness tension is unavoidable, i.e., achieving both objectives simultaneously requires carefully balanced compromises rather than optimization of either in isolation. The source code for our proposed algorithm is publicly accessible at https://github.com/szpsunkk/FedPF.