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Non-collaborative dialogue involves two participants with conflicting interests engaging in a multi-round dialogue to achieve their own goals. Strategy planning is the key to guiding both participants towards a consensus. Most LLMs-based methods use stimulus prompts or external strategy planners for strategy planning. However, stimulus prompts fail to teach LLMs to plan dialogue strategies explicitly. Moreover, training external strategy planners doesn’t fully account for adversarial interactions, thereby limiting their effectiveness against tough resisters. In this paper, to mitigate the above issues, we propose GAIA, a Game-based Adversarial self-play InterActive training paradigm, which constructs an adversarial two-player (a persuader and a resister) zero-sum game and guides the game to approximate Nash Equilibrium (NE) via reinforcement learning (RL) for the non-collaborative dialogues. First, we design a Chain-of-Mind prompt to reason the resister’s dialogue act step-by-step to plan the persuasive strategies. Secondly, to adversarially improve the persuader, we construct diverse resistant planners and theoretically improve the persuader’s optimal lower bound. Finally, we iteratively optimise their policies via adversarial self-play interactive RL and design an 𝜖-NE verification algorithm to approximate the game’s NE. Experiments on three datasets show that our model obtains state-of-the-art performance.