Large Language Models (LLMs) are increasingly deployed as autonomous agents that solve tasks through multi-step interactions. However, most post-training methods are designed for single-turn reasoning or instruction-following tasks and provide limited supervision for long-horizon conversational decision making. In this work, we investigate whether Self-Correction via Reinforcement Learning (SCoRe), originally proposed for single-step mathematical reasoning and code generation, can improve agentic performance in multi-turn dialogue games. We adapt SCoRe to the PLAYPEN benchmark by fine-tuning Qwen3.5-9B on five single-player dialogue games using interaction-level rewards and iterative self-correction. Experimental results show that the resulting model substantially improves performance on the trained single-player games and further generalizes to unseen multi-player dialogue games, increasing the overall ClemScore from 41.18 to 43.31. Although a slight decrease is observed on the aggregate StatScore, the model largely retains its general language understanding and reasoning capabilities. These findings demonstrate that self-correction reinforcement learning is an effective approach for improving long-horizon conversational agent behavior beyond single-step reasoning tasks.