  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.
