  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
privacy game (FLPG), 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 FLPG 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}.
