Large language model (LLM) agents have shown remarkable progress in social deduction games (SDGs). However, existing approaches primarily focus on information processing and strategy selection, overlooking the significance of persuasive communication in influencing other players' beliefs and responses. In SDGs, success depends not only on making correct deductions but on convincing others to response in alignment with one's intent. To address this limitation, we formalize turn-based dialogue in SDGs as a Stackelberg competition, where the current player acts as the leader who strategically influences the follower's response. Building on this theoretical foundation, we propose a reinforcement learning framework that trains agents to optimize utterances for persuasive impact. Through comprehensive experiments across three diverse SDGs, we demonstrate that our agents significantly outperform baselines. This work represents a significant step toward developing AI agents capable of strategic social influence, with implications extending to scenarios requiring persuasive communication. Our code and data are available at https://3dagentworld.github.io/leader_follower.