Observer, Not Player: Simulating Theory of Mind in LLMs through Game Observation

2025-12-22

AI Summary

This paper investigates whether large language models (LLMs) possess theory-of-mind (ToM)-like sequential behavioral reasoning in strategic simple games (e.g., Rock-Paper-Scissors), specifically from an *observer*—rather than *agent*—perspective, focusing on strategy recognition and attribution. Method: We propose the first interactive ToM evaluation framework featuring: (i) a lightweight dynamic strategy generator; (ii) an interpretable Strategy Identification Rate (SIR) metric; and (iii) a real-time reasoning溯源 module. We introduce Union Loss—a unified metric integrating calibration, sensitivity, and payoff alignment—quantified via cross-entropy, Brier score, and expected-value discrepancy. Contribution/Results: Our framework robustly discriminates LLMs’ ToM capabilities under static versus dynamic opponent strategies. It establishes an open-source, reproducible, and highly transparent benchmark for evaluating ToM-enabled agents, enabling fine-grained, behaviorally grounded assessment of mental-state inference in strategic interaction.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

We present an interactive framework for evaluating whether large language models (LLMs) exhibit genuine "understanding" in a simple yet strategic environment. As a running example, we focus on Rock-Paper-Scissors (RPS), which, despite its apparent simplicity, requires sequential reasoning, adaptation, and strategy recognition. Our system positions the LLM as an Observer whose task is to identify which strategies are being played and to articulate the reasoning behind this judgment. The purpose is not to test knowledge of Rock-Paper-Scissors itself, but to probe whether the model can exhibit mind-like reasoning about sequential behavior. To support systematic evaluation, we provide a benchmark consisting of both static strategies and lightweight dynamic strategies specified by well-prompted rules. We quantify alignment between the Observer's predictions and the ground-truth distributions induced by actual strategy pairs using three complementary signals: Cross-Entropy, Brier score, and Expected Value (EV) discrepancy. These metrics are further integrated into a unified score, the Union Loss, which balances calibration, sensitivity, and payoff alignment. Together with a Strategy Identification Rate (SIR) metric, our framework captures not only predictive accuracy but also whether the model can stably identify the latent strategies in play. The demo emphasizes interactivity, transparency, and reproducibility. Users can adjust LLM distributions in real time, visualize losses as they evolve, and directly inspect reasoning snippets to identify where and why failures occur. In doing so, our system provides a practical and interpretable proxy for mind-like inference in sequential games, offering insights into both the strengths and limitations of current LLM reasoning.

Problem

• Evaluates LLMs' understanding in strategic game environments
• Probes mind-like reasoning about sequential behavior in models
• Measures predictive accuracy and strategy identification in games

Innovation

• Observer framework for LLM reasoning evaluation
• Benchmark with static and dynamic strategy specifications
• Unified Union Loss metric integrating multiple evaluation signals