By allowing users to erase their data's impact on federated learning models, federated unlearning protects users' right to be forgotten and data privacy. Despite a burgeoning body of research on federated unlearning's technical feasibility, there is a paucity of literature investigating the considerations behind users' requests for data revocation. This paper proposes a non-cooperative game framework to study users' data revocation strategies in federated unlearning. We prove the existence of a Nash equilibrium. However, users' best response strategies are coupled via model performance and unlearning costs, which makes the equilibrium computation challenging. We obtain the Nash equilibrium by establishing its equivalence with a much simpler auxiliary optimization problem. We also summarize users' multi-dimensional attributes into a single-dimensional metric and derive the closed-form characterization of an equilibrium, when users' unlearning costs are negligible. Moreover, we compare the cases of allowing and forbidding partial data revocation in federated unlearning. Interestingly, the results reveal that allowing partial revocation does not necessarily increase users' data contributions or payoffs due to the game structure. Additionally, we demonstrate that positive externalities may exist between users' data revocation decisions when users incur unlearning costs, while this is not the case when their unlearning costs are negligible.

翻译：通过允许用户消除其数据对联邦学习模型的影响，联邦遗忘保护了用户的被遗忘权与数据隐私。尽管关于联邦遗忘技术可行性的研究日益增多，但探讨用户数据撤销请求背后动机的文献仍十分匮乏。本文提出一个非合作博弈框架以研究用户在联邦遗忘中的数据撤销策略，并证明纳什均衡的存在性。然而，用户的最优响应策略通过模型性能与遗忘成本相互耦合，使得均衡计算极具挑战性。我们通过将纳什均衡等价转化为一个更简洁的辅助优化问题来实现求解，并在用户遗忘成本可忽略时，将用户的多维属性归纳为单维度量，进而推导出均衡的闭式表征。此外，本文比较了联邦遗忘中允许与禁止部分数据撤销两种情形。有趣的是，结果表明：由于博弈结构特性，允许部分撤销未必能提升用户的数据贡献或收益。同时，我们证明当用户承担遗忘成本时，用户间的数据撤销决策可能存在正外部性，而当遗忘成本可忽略时则不存在该现象。