Vince Trencsenyi

Agnieszka Mensfelt, Kostas Stathis, Vince Trencsenyi

Game theory is a powerful framework for reasoning about strategic interactions, with applications in domains ranging from day-to-day life to international politics. However, applying formal reasoning tools in such contexts is challenging, as these scenarios are often expressed in natural language. To address this, we introduce a framework for the autoformalization of game-theoretic scenarios, which translates natural language descriptions into formal logic representations suitable for formal solvers. Our approach utilizes one-shot prompting and a solver that provides feedback on syntactic correctness to allow LLMs to refine the code. We evaluate the framework using GPT-4o and a dataset of natural language problem descriptions, achieving 98% syntactic correctness and 88% semantic correctness. These results show the potential of LLMs to bridge the gap between real-life strategic interactions and formal reasoning.

Agnieszka Mensfelt, Kostas Stathis, Vince Trencsenyi

Large language models (LLMs) are increasingly explored as general-purpose reasoners, particularly in agentic contexts. However, their outputs remain prone to mathematical and logical errors. This is especially challenging in open-ended tasks, where unstructured outputs lack explicit ground truth and may contain subtle inconsistencies. To address this issue, we propose Logic-Enhanced Language Model Agents (LELMA), a framework that integrates LLMs with formal logic to enable validation and refinement of natural language reasoning. LELMA comprises three components: an LLM-Reasoner, an LLM-Translator, and a Solver, and employs autoformalization to translate reasoning into logic representations, which are then used to assess logical validity. Using game-theoretic scenarios such as the Prisoner's Dilemma as testbeds, we highlight the limitations of both less capable (Gemini 1.0 Pro) and advanced (GPT-4o) models in generating logically sound reasoning. LELMA achieves high accuracy in error detection and improves reasoning correctness via self-refinement, particularly in GPT-4o. The study also highlights challenges in autoformalization accuracy and in evaluation of inherently ambiguous open-ended reasoning tasks.

Agnieszka Mensfelt, Adarsh Prabhakaran, Adrian Haret et al.

Frontier reasoning-tuned language models still fail on deductive tasks at depth, and the cost of improved performance through extended internal reasoning scales poorly. Symbolic delegation offers a complementary route: a language model translates the problem, while a solver performs the inference. However, current autoformalization pipelines for logic programming are typically bespoke integrations tied to particular tasks or agents. We introduce PrologMCP, a task-agnostic, open-source server that exposes Prolog as a stateful tool through the Model Context Protocol (MCP). Its compact tool interface, structured error reporting, and per-session isolation make the translate-run-inspect-repair loop a reusable primitive for MCP-capable agents. We evaluate a formalizer agent enhanced with PrologMCP against standard and reasoning LLMs (Claude Sonnet 4.6, GPT-4.1, and o4-mini) on two subsets of PARARULE-Plus: a general-purpose sample and a more challenging one targeting a specific failure mode of natural-language reasoning. On the general sample, the formalizer matches or exceeds reasoning LLMs (accuracy 1.00 vs.\ 1.00 / 0.998), with the largest gains over standard models (0.762 for GPT-4.1). On the challenging subset, the formalizer remains near-perfect (1.00 / 0.99) while reasoning LLMs drop to 0.95 / 0.94. These results suggest that delegating inference to Prolog via MCP is a robust and inspectable alternative to extended natural-language reasoning.

Vince Trencsenyi

Differences in perception, information asymmetries, and bounded rationality lead game-theoretic players to derive a private, subjective view of the game that may diverge from the underlying ground-truth scenario and may be misaligned with other players' interpretations. While typical game-theoretic assumptions often overlook such heterogeneity, hypergame theory provides the mathematical framework to reason about mismatched mental models. Although hypergames have recently gained traction in dynamic applications concerning uncertainty, their practical adoption in multi-agent system research has been hindered by the lack of a unifying, formal, and practical representation language, as well as scalable algorithms for managing complex hypergame structures and equilibria. Our work addresses this gap by introducing a declarative, logic-based domain-specific language for encoding hypergame structures and hypergame solution concepts. Leveraging answer-set programming, we develop an automated pipeline for instantiating hypergame structures and running our novel hypergame rationalisation procedure, a mechanism for finding belief structures that justify seemingly irrational outcomes. The proposed language establishes a unifying formalism for hypergames and serves as a foundation for developing nuanced, belief-based heterogeneous reasoners, offering a verifiable context with logical guarantees. Together, these contributions establish the connection between hypergame theory, multi-agent systems, and strategic AI.

Vince Trencsenyi, Agnieszka Mensfelt, Kostas Stathis

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.

Vince Trencsenyi, Agnieszka Mensfelt, Kostas Stathis

The rapid rise of large language models (LLMs) has shifted artificial intelligence (AI) research toward agentic systems, motivating the use of weaker and more flexible notions of agency. However, this shift raises key questions about the extent to which LLM-based agents replicate human strategic reasoning, particularly in game-theoretic settings. In this context, we examine the role of agentic sophistication in shaping artificial reasoners' performance by evaluating three agent designs: a simple game-theoretic model, an unstructured LLM-as-agent model, and an LLM integrated into a traditional agentic framework. Using guessing games as a testbed, we benchmarked these agents against human participants across general reasoning patterns and individual role-based objectives. Furthermore, we introduced obfuscated game scenarios to assess agents' ability to generalise beyond training distributions. Our analysis, covering over 2000 reasoning samples across 25 agent configurations, shows that human-inspired cognitive structures can enhance LLM agents' alignment with human strategic behaviour. Still, the relationship between agentic design complexity and human-likeness is non-linear, highlighting a critical dependence on underlying LLM capabilities and suggesting limits to simple architectural augmentation.

Agnieszka Mensfelt, Kostas Stathis, Vince Trencsenyi

Multi-agent simulations are versatile tools for exploring interactions among natural and artificial agents, but their development typically demands domain expertise and manual effort. This work introduces the Generative Agents for Multi-Agent Autoformalization (GAMA) framework, which automates the formalization of interaction scenarios in simulations using agents augmented with large language models (LLMs). To demonstrate the application of GAMA, we use natural language descriptions of game-theoretic scenarios representing social interactions, and we autoformalize them into executable logic programs defining game rules, with syntactic correctness enforced through a solver-based validation. To ensure runtime validity, an iterative, tournament-based procedure tests the generated rules and strategies, followed by exact semantic validation when ground truth outcomes are available. In experiments with 110 natural language descriptions across five 2x2 simultaneous-move games, GAMA achieves 100% syntactic and 76.5% semantic correctness with Claude 3.5 Sonnet, and 99.82% syntactic and 77% semantic correctness with GPT-4o. The framework also shows high semantic accuracy in autoformalizing agents' strategies.