Solver-Guided Reasoning for Mixed-Equilibrium Strategies

• URL: http://arxiv.org/abs/2608.06741v1
• Date: Fri, 07 Aug 2026 03:12:06 GMT
• Title: Solver-Guided Reasoning for Mixed-Equilibrium Strategies
• Abstract summary: Mixed-Strategy Decision Tree (MDT) articulates the silent optimality of the equilibrium into sparse strategic rules.<n>We instantiate this study on No-Limit Texas Hold'em by querying a solver oracle for over textbf250 million mixed-strategy decisions.
• Score: 38.03807500614725
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reasoning in large language models (LLMs) is often grounded in human text, human demonstrations, and human-generated rationales. For equilibrium reasoning in complex games, however, relying on human data can be suboptimal. In fact, human play is often guided by intuition and heuristics and can deviate substantially from game equilibrium. This discrepancy is amplified in games with mixed-strategy equilibria, where human data is heavily biased toward pure strategies. Consequently, conditioning LLMs on this data yields weak game strategies. To grant LLMs the reasoning capacity in games, in this work, we study how to elicit equilibrium play using solver output. We propose Mixed-Strategy Decision Tree (MDT), which articulates the silent optimality of the equilibrium into sparse strategic rules that both humans and LLMs could understand. Using solver output rather than human annotation allows us to extend the input to arbitrarily new states and continuations. We instantiate this study on No-Limit Texas Hold'em by querying a solver oracle for over \textbf{250 million mixed-strategy decisions}; MDT together with other techniques \textbf{reduces the $\ell_1$ distance to the equilibrium by $52.6\%$} across $8$ different LLM configurations. A Route-only ablation tests the incremental contribution of the shadow-based contrast, while complete River-endgame and Liar's Dice experiments evaluate strategic fidelity and portability beyond the original NLH communication setting.

Related papers

• Beyond Survival: Evaluating LLMs in Social Deduction Games with Human-Aligned Strategies [54.08697738311866]
  Social deduction games like Werewolf combine language, reasoning, and strategy.<n>We curate a high-quality, human-verified multimodal Werewolf dataset containing over 100 hours of video, 32.4M utterance tokens, and 15 rule variants.<n>We propose a novel strategy-alignment evaluation that leverages the winning faction's strategies as ground truth in two stages.
  arXiv  Detail & Related papers  (2025-10-13T13:33:30Z)
• LLMs as Policy-Agnostic Teammates: A Case Study in Human Proxy Design for Heterogeneous Agent Teams [0.7734726150561086]
  A critical challenge in modelling Heterogeneous-Agent Teams is training agents to collaborate with teammates whose policies are inaccessible or non-stationary, such as humans.<n>Traditional approaches rely on expensive human-in-the-loop data, which limits scalability.<n>We propose using Large Language Models (LLMs) as policy-agnostic human proxies to generate synthetic data that mimics human decision-making.
  arXiv  Detail & Related papers  (2025-10-07T17:21:20Z)
• Who is a Better Player: LLM against LLM [53.46608216197315]
  We propose an adversarial benchmarking framework to assess the comprehensive performance of Large Language Models (LLMs) through board games competition.<n>We introduce Qi Town, a specialized evaluation platform that supports 5 widely played games and involves 20 LLM-driven players.
  arXiv  Detail & Related papers  (2025-08-05T06:41:47Z)
• Do LLMs Know When to Flip a Coin? Strategic Randomization through Reasoning and Experience [1.7223564681760168]
  Strategic randomization is a key principle in game theory, yet it remains underexplored in large language models (LLMs)<n>We propose a novel zero-sum game inspired by the Tian Ji Horse Race, where the Nash equilibrium corresponds to a maximal entropy strategy.<n>We show that weaker models remain deterministic regardless of prompts, while stronger models exhibit increased randomization under explicit hints.
  arXiv  Detail & Related papers  (2025-06-21T05:26:33Z)
• GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations [87.99872683336395]
  Large Language Models (LLMs) are integrated into critical real-world applications. This paper evaluates LLMs' reasoning abilities in competitive environments. We first propose GTBench, a language-driven environment composing 10 widely recognized tasks.
  arXiv  Detail & Related papers  (2024-02-19T18:23:36Z)
• Neural Population Learning beyond Symmetric Zero-sum Games [52.20454809055356]
  We introduce NeuPL-JPSRO, a neural population learning algorithm that benefits from transfer learning of skills and converges to a Coarse Correlated (CCE) of the game. Our work shows that equilibrium convergent population learning can be implemented at scale and in generality.
  arXiv  Detail & Related papers  (2024-01-10T12:56:24Z)
• ApproxED: Approximate exploitability descent via learned best responses [61.17702187957206]
  We study the problem of finding an approximate Nash equilibrium of games with continuous action sets. We propose two new methods that minimize an approximation of exploitability with respect to the strategy profile.
  arXiv  Detail & Related papers  (2023-01-20T23:55:30Z)
• Finding mixed-strategy equilibria of continuous-action games without gradients using randomized policy networks [83.28949556413717]
  We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. We model players' strategies using artificial neural networks. This paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.
  arXiv  Detail & Related papers  (2022-11-29T05:16:41Z)
• A Genetic Algorithm approach to Asymmetrical Blotto Games with Heterogeneous Valuations [0.0]
  Blotto Games are a popular model of multi-dimensional strategic resource allocation. We introduce a genetic algorithm inspired from biological evolution, interpreted as social learning, to solve this problem. We show that our genetic algorithm converges to the analytical Nash equilibrium of the symmetric Blotto game.
  arXiv  Detail & Related papers  (2021-03-26T10:20:19Z)
• Hindsight and Sequential Rationality of Correlated Play [18.176128899338433]
  We look at algorithms that ensure strong performance in hindsight relative to what could have been achieved with modified behavior. We develop and advocate for this hindsight framing of learning in general sequential decision-making settings. We present examples illustrating the distinct strengths and weaknesses of each type of equilibrium in the literature.
  arXiv  Detail & Related papers  (2020-12-10T18:30:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.