Multi-agent systems utilizing large language models (LLMs) have shown great promise in achieving natural dialogue. However, smooth dialogue control and autonomous decision making among agents still remain challenges. In this study, we focus on conversational norms such as adjacency pairs and turn-taking found in conversation analysis and propose a new framework called "Murder Mystery Agents" that applies these norms to AI agents' dialogue control. As an evaluation target, we employed the "Murder Mystery" game, a reasoning-type table-top role-playing game that requires complex social reasoning and information manipulation. In this game, players need to unravel the truth of the case based on fragmentary information through cooperation and bargaining. The proposed framework integrates next speaker selection based on adjacency pairs and a self-selection mechanism that takes agents' internal states into account to achieve more natural and strategic dialogue. To verify the effectiveness of this new approach, we analyzed utterances that led to dialogue breakdowns and conducted automatic evaluation using LLMs, as well as human evaluation using evaluation criteria developed for the Murder Mystery game. Experimental results showed that the implementation of the next speaker selection mechanism significantly reduced dialogue breakdowns and improved the ability of agents to share information and perform logical reasoning. The results of this study demonstrate that the systematics of turn-taking in human conversation are also effective in controlling dialogue among AI agents, and provide design guidelines for more advanced multi-agent dialogue systems.