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

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.

Autoformalizing and Simulating Game-Theoretic Scenarios using LLM-augmented Agents

Game-theoretic simulations are a versatile tool for exploring interactions of both natural and artificial agents. However, modelling real-world scenarios and developing simulations often require substantial human expertise and effort. To streamline this process, we present a framework that enables the autoformalization of game-theoretic scenarios using agents augmented by large language models (LLMs). In this approach, LLM-augmented agents translate natural language scenario descriptions into executable logic programs that define the rules of each game, validating these programs for syntactic accuracy. A tournament simulation is then conducted, during which the agents test the functionality of the generated games by playing them. When a ground truth payoff matrix is available, an exact semantic validation can also be performed. The validated games can then be used in further simulations to assess the effectiveness of different strategies. We evaluate our approach on a diverse set of 55 natural language descriptions across five well-known 2x2 simultaneous-move games, demonstrating 96% syntactic and 87% semantic correctness in the generated game rules. Additionally, we assess the LLM-augmented agents' capability to autoformalize strategies for gameplay.

Logic-Enhanced Language Model Agents for Trustworthy Social Simulations

We introduce the Logic-Enhanced Language Model Agents (LELMA) framework, a novel approach to enhance the trustworthiness of social simulations that utilize large language models (LLMs). While LLMs have gained attention as agents for simulating human behaviour, their applicability in this role is limited by issues such as inherent hallucinations and logical inconsistencies. LELMA addresses these challenges by integrating LLMs with symbolic AI, enabling logical verification of the reasoning generated by LLMs. This verification process provides corrective feedback, refining the reasoning output. The framework consists of three main components: an LLM-Reasoner for producing strategic reasoning, an LLM-Translator for mapping natural language reasoning to logic queries, and a Solver for evaluating these queries. This study focuses on decision-making in game-theoretic scenarios as a model of human interaction. Experiments involving the Hawk-Dove game, Prisoner's Dilemma, and Stag Hunt highlight the limitations of state-of-the-art LLMs, GPT-4 Omni and Gemini 1.0 Pro, in producing correct reasoning in these contexts. LELMA demonstrates high accuracy in error detection and improves the reasoning correctness of LLMs via self-refinement, particularly in GPT-4 Omni.