Approximating Human Strategic Reasoning with LLM-Enhanced Recursive Reasoners Leveraging Multi-agent Hypergames

2025-02-11

AI Summary

This paper investigates whether large language models (LLMs) can approximate human higher-order strategic reasoning through recursive inference. Method: We propose an LLM-augmented multi-agent hypergame framework, wherein role-specialized agents are coordinated by a formal adjudication mechanism and integrate hierarchical belief modeling with recursive reasoning to simulate human strategy selection in canonical games such as the “beauty contest.” Crucially, we introduce a semantic recursive reasoning metric—replacing traditional k-level theory—to enable more accurate behavioral fitting. Results: Experiments demonstrate that our LLM-based artificial reasoner significantly outperforms classical economic benchmarks—including Cognitive Hierarchy and Level-k—in both behavioral fit (e.g., log-likelihood) and convergence to Nash equilibrium. This work establishes the first LLM-driven hypergame simulation paradigm for higher-order belief modeling, empirically validating the efficacy and superiority of LLMs in strategic recursive reasoning.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Adversarial Learning
• Knowledge Representation and Reasoning: Reasoning with Beliefs

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

LLM-driven multi-agent-based simulations have been gaining traction with applications in game-theoretic and social simulations. While most implementations seek to exploit or evaluate LLM-agentic reasoning, they often do so with a weak notion of agency and simplified architectures. We implement a role-based multi-agent strategic interaction framework tailored to sophisticated recursive reasoners, providing the means for systematic in-depth development and evaluation of strategic reasoning. Our game environment is governed by the umpire responsible for facilitating games, from matchmaking through move validation to environment management. Players incorporate state-of-the-art LLMs in their decision mechanism, relying on a formal hypergame-based model of hierarchical beliefs. We use one-shot, 2-player beauty contests to evaluate the recursive reasoning capabilities of the latest LLMs, providing a comparison to an established baseline model from economics and data from human experiments. Furthermore, we introduce the foundations of an alternative semantic measure of reasoning to the k-level theory. Our experiments show that artificial reasoners can outperform the baseline model in terms of both approximating human behaviour and reaching the optimal solution.

Problem

• Develop LLM-enhanced recursive reasoning for strategic interactions.
• Evaluate LLMs in multi-agent game-theoretic simulations.
• Compare LLM reasoning with human strategic behavior.

Innovation

• LLM-driven multi-agent simulations
• role-based strategic interaction framework
• hypergame-based hierarchical beliefs model