Do Reasoning Models Ask Better Questions? A Formal Information-Theoretic Analysis on Multi-Turn LLM Games

Large Language Models (LLMs) excel at many tasks but still struggle with a critical ability for LLM-based agents: asking good questions for resolving ambiguity in user requests. While prior work has explored information-seeking behavior through word games, existing benchmarks lack comprehensive evaluation frameworks that provide both final and intermediate signals based on Information Gain (IG). Moreover, they rarely provide systematic comparisons between models that use chain-of-thought reasoning and those that do not. We propose a multi-turn dialogue framework that quantitatively measures how effectively LLMs gather information through yes/no questions in a hierarchical knowledge graph environment. Our framework employs a triad of interacting LLM agents that ask questions, answer them, and update the hypothesis space. We adopt IG as the main metric, grounded in Shannon entropy, to assess query effectiveness at each turn and cumulatively. We instantiate our framework in a geographical Guess My City game setting organized in a five-level taxonomy and evaluate multiple LLM variants under fully and partially observable conditions, with and without Chain-of-Thought reasoning. Our experiments demonstrate that, among the evaluated models, the ones with explicit reasoning capabilities achieve higher IG per turn and reach solutions in fewer steps, particularly in partially observable settings. Analysis of reasoning traces reveals that smaller models compensate for limited capacity through more aggressive exploration of candidate questions, while larger models exhibit higher assertiveness in selecting optimal queries, generating candidates with greater potential IG.