Level design is central to shaping the player experience by structuring gameplay progression, balancing difficulty, and maintaining engagement. Traditional approaches to level parameter design—ranging from heuristic-driven theoretical models to data-intensive empirical models—demand extensive manual effort and expert knowledge. In this paper, we present AI Game Designer, a novel prototype system that leverages Large Language Models (LLM)-based agents to automate game level balancing. By formulating the task as a Markov Decision Process (MDP), the system integrates simulation-based evaluation with LLM-guided reasoning to iteratively adjust the level parameters in response to performance feedback. The agent interprets the statistical outputs of large-scale simulations and applies structured and interpretable reasoning to refine design decisions, enabling effective optimization without reliance on handcrafted rules. The system features a web-based graphical interface to support both fully automated workflows and human-in-the-loop collaboration, improving usability, transparency, and adaptability in real-world level design scenarios.