In human-AI interaction, a prominent goal is to attain human's desirable outcome with the assistance of AI agents, which can be ideally delineated as a problem of seeking the optimal Nash Equilibrium that matches the human's desirable outcome. However, reaching the outcome is usually challenging due to the existence of multiple Nash Equilibria that are related to the assisting task but do not correspond to the human's desirable outcome. To tackle this issue, we employ a theoretical framework called structural causal game (SCG) to formalize the human-AI interactive process. Furthermore, we introduce a strategy referred to as pre-policy intervention on the SCG to steer AI agents towards attaining the human's desirable outcome. In more detail, a pre-policy is learned as a generalized intervention to guide the agents' policy selection, under a transparent and interpretable procedure determined by the SCG. To make the framework practical, we propose a reinforcement learning-like algorithm to search out this pre-policy. The proposed algorithm is tested in both gridworld environments and realistic dialogue scenarios with large language models, demonstrating its adaptability in a broader class of problems and potential effectiveness in real-world situations.