In federated learning, benign participants aim to optimize a global model collaboratively. However, the risk of \textit{privacy leakage} cannot be ignored in the presence of \textit{semi-honest} adversaries. Existing research has focused either on designing protection mechanisms or on inventing attacking mechanisms. While the battle between defenders and attackers seems never-ending, we are concerned with one critical question: is it possible to prevent potential attacks in advance? To address this, we propose the first game-theoretic framework that considers both FL defenders and attackers in terms of their respective payoffs, which include computational costs, FL model utilities, and privacy leakage risks. We name this game the Federated Learning Security Game (FLSG), in which neither defenders nor attackers are aware of all participants' payoffs. To handle the \textit{incomplete information} inherent in this situation, we propose associating the FLSG with an \textit{oracle} that has two primary responsibilities. First, the oracle provides lower and upper bounds of the payoffs for the players. Second, the oracle acts as a correlation device, privately providing suggested actions to each player. With this novel framework, we analyze the optimal strategies of defenders and attackers. Furthermore, we derive and demonstrate conditions under which the attacker, as a rational decision-maker, should always follow the oracle's suggestion \textit{not to attack}.

翻译：在联邦学习中，善意参与者旨在协作优化全局模型。然而，在存在半诚实对手的情况下，隐私泄露风险不可忽视。现有研究要么聚焦于设计保护机制，要么专注于发明攻击机制。尽管防御者与攻击者之间的斗争似乎永无止境，我们关注一个关键问题：是否可能提前预防潜在攻击？为此，我们提出了首个博弈论框架，该框架同时考虑联邦学习防御者和攻击者各自的收益，包括计算成本、联邦学习模型效用和隐私泄露风险。我们将该博弈命名为联邦学习安全博弈，其中防御者和攻击者均无法获知所有参与者的收益。为应对这种情况固有的不完全信息，我们提出将联邦学习安全博弈与一个具有两项主要职责的预言机相关联。首先，预言机为参与者提供收益的下界和上界。其次，预言机作为关联设备，私下向每位参与者提供建议行动。通过这一新颖框架，我们分析了防御者和攻击者的最优策略。此外，我们推导并证明了在何种条件下，作为理性决策者的攻击者应始终遵循预言机的建议不发动攻击。