mlsanityData to 14 Oct 2026

Steering Language Models with Game-Theoretic Solvers

arXiv 2402.01704 ↗First posted 24 Jan 2024cs.CL cs.AI cs.GTcited by 28

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Abstract (arXiv)

Mathematical models of interactions among rational agents have long been studied in game theory. However these interactions are often over a small set of discrete game actions which is very different from how humans communicate in natural language. To bridge this gap, we introduce a framework that allows equilibrium solvers to work over the space of natural language dialogue generated by large language models (LLMs). Specifically, by modelling the players, strategies and payoffs in a "game" of dialogue, we create a binding from natural language interactions to the conventional symbolic logic of game theory. Given this binding, we can ask existing game-theoretic algorithms to provide us with strategic solutions (e.g., what string an LLM should generate to maximize payoff in the face of strategic partners or opponents), giving us predictors of stable, rational conversational strategies. We focus on three domains that require different negotiation strategies: scheduling meetings, trading fruit and debate, and evaluate an LLM's generated language when guided by solvers. We see that LLMs that follow game-theory solvers result in dialogue generations that are less exploitable than the control (no guidance from solvers), and the language generated results in higher rewards, in all negotiation domains. We discuss future implications of this work, and how game-theoretic solvers that can leverage the expressivity of natural language can open up a new avenue of guiding language research.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 29 of its 50 references that are in the map. First posted on arXiv 24 Jan 2024.

Builds on

29 of 50 references.

References · 29

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2023Toolformer: Language Models Can Teach Themselves to Use Toolscited by 4,182
  3. 2023Mistral 7Bcited by 3,164
  4. 2023PaLM 2 Technical Reportcited by 1,162
  5. 2023Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Promptingcited by 1,122
  6. 2019How Can We Know What Language Models Know?cited by 959
  7. 2022STaR: Bootstrapping Reasoning With Reasoningcited by 940
  8. 2021Show Your Work: Scratchpads for Intermediate Computation with Language Modelscited by 886
  9. 2023Large Language Models as Optimizerscited by 864
  10. 2023Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolutioncited by 551
  11. 2022MineDojo: Building Open-Ended Embodied Agents with Internet-Scale Knowledgecited by 478
  12. 2018AI safety via debatecited by 400
17 more
  1. 2019Explain Yourself! Leveraging Language Models for Commonsense Reasoningcited by 367
  2. 2021Do Prompt-Based Models Really Understand the Meaning of their Prompts?cited by 326
  3. 2017A Unified Game-Theoretic Approach to Multiagent Reinforcement Learningcited by 268
  4. 2023Reward Design with Language Modelscited by 261
  5. 2023AI Deception: A Survey of Examples, Risks, and Potential Solutionscited by 188
  6. 2019OpenSpiel: A Framework for Reinforcement Learning in Gamescited by 186
  7. 2020Unsupervised Commonsense Question Answering with Self-Talkcited by 161
  8. 2020The Complexity of Constrained Min-Max Optimizationcited by 82
  9. 2023Strategic Reasoning with Language Modelscited by 64
  10. 2023Scalable AI Safety via Doubly-Efficient Debatecited by 57
  11. 2023The Consensus Game: Language Model Generation via Equilibrium Searchcited by 36
  12. 2024The illusion of artificial inclusioncited by 34
  13. 2021Attention Flows are Shapley Value Explanationscited by 30
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  15. 2023Be Selfish, But Wisely: Investigating the Impact of Agent Personality in Mixed-Motive Human-Agent Interactionscited by 15
  16. 2022Pragmatics in Language Grounding: Phenomena, Tasks, and Modeling Approachescited by 12
  17. 2023Online Learning and Solving Infinite Games with an ERM Oraclecited by 11

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 14; 2026: 8.

28 papers.

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  1. 2025Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systemscited by 126
  2. 2024Emergent social conventions and collective bias in LLM populationscited by 123
  3. 2024LLM as a Mastermind: A Survey of Strategic Reasoning with Large Language Modelscited by 99
  4. 2024Game-theoretic LLM: Agent Workflow for Negotiation Gamescited by 56
  5. 2025Will Systems of LLM Agents Cooperate: An Investigation into a Social Dilemmacited by 25
  6. 2025Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontierscited by 16
  7. 2024Efficacy of Language Model Self-Play in Non-Zero-Sum Gamescited by 15
  8. 2025Reevaluating Policy Gradient Methods for Imperfect-Information Gamescited by 13
  9. 2024Policy Space Response Oracles: A Surveycited by 10
  10. 2025EPO: Explicit Policy Optimization for Strategic Reasoning in LLMs via Reinforcement Learningcited by 8
  11. 2025From Natural Language to Extensive-Form Game Representationscited by 6
  12. 2024Enhancing Language Model Rationality with Bi-Directional Deliberation Reasoningcited by 5
16 more
  1. 2025Multiplayer Federated Learning: Reaching Equilibrium with Less Communicationcited by 5
  2. 2025Do LLMs Strategically Reveal, Conceal, and Infer Information? A Theoretical and Empirical Analysis in The Chameleon Gamecited by 5
  3. 2026Distilling Game Code World Model Generation into Lightweight Large Language Modelscited by 5
  4. 2025Utility-inspired Reward Transformations Improve Reinforcement Learning Training of Language Modelscited by 2
  5. 2025The Power of Stories: Narrative Priming Shapes How LLM Agents Collaborate and Competecited by 2
  6. 2026Code-Space Response Oracles: Generating Interpretable Multi-Agent Policies with Large Language Modelscited by 2
  7. 2025Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Modelscited by 1
  8. 2025Make an Offer They Can't Refuse: Grounding Bayesian Persuasion in Real-World Dialogues without Pre-Commitmentcited by 1
  9. 2026Game of Thought: Robust Information Seeking with Large Language Models Using Game Theorycited by 1
  10. 2025Safety Game: Inference-Time Alignment of Black-Box LLMs via Constrained Optimizationcited by 0
  11. 2025Agentmandering: A Game-Theoretic Framework for Fair Redistricting via Large Language Model Agentscited by 0
  12. 2026LLM Active Alignment: A Nash Equilibrium Perspectivecited by 0
  13. 2026Communicate-Predict-Act: Evaluating Social Intelligence of Agentscited by 0
  14. 2026How a Cooperative-Override Circuit Suppresses Nash Play in Large Language Modelscited by 0
  15. 2026Strategy, Not Payoffs: A Behavioural Embedding of Normal-Form Gamescited by 0
  16. 2026AI Alignment through a Game-theoretic Lens: A Surveycited by 0