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，但探讨用户数据撤回请求背后决策因素的文献仍较为匮乏。本文提出一个非合作博弈框架来研究联邦遗忘中用户的数据撤回策略。我们证明了纳什均衡的存在性。然而，用户的最佳响应策略通过模型性能与遗忘成本相互耦合，这使得均衡计算面临挑战。通过建立该均衡与一个更简单的辅助优化问题之间的等价性，我们推导出了纳什均衡。此外，当用户遗忘成本可忽略时，我们将用户的多维属性归纳为单维度度量指标，并给出了均衡的闭式解。本文还对比了联邦遗忘中允许与禁止部分数据撤回两种情形。有趣的是，结果表明由于博弈结构的存在，允许部分撤回并不必然增加用户的数据贡献或收益。我们进一步证明，当用户承担遗忘成本时，用户间的数据撤回决策可能存在正外部性，而当遗忘成本可忽略时则不存在这一现象。