Credence Calibration Game? Calibrating Large Language Models through Structured Play

As Large Language Models (LLMs) are increasingly deployed in decision-critical domains, it becomes essential to ensure that their confidence estimates faithfully correspond to their actual correctness. Existing calibration methods have primarily focused on post-hoc adjustments or auxiliary model training; however, many of these approaches necessitate additional supervision or parameter updates. In this work, we propose a novel prompt-based calibration framework inspired by the Credence Calibration Game. Our method establishes a structured interaction loop wherein LLMs receive feedback based on the alignment of their predicted confidence with correctness. Through feedback-driven prompting and natural language summaries of prior performance, our framework dynamically improves model calibration. Extensive experiments across models and game configurations demonstrate consistent improvements in evaluation metrics. Our results highlight the potential of game-based prompting as an effective strategy for LLM calibration. Code and data are available at https://anonymous.4open.science/r/LLM-Calibration/.