mlsanityData to 7 Oct 2026

The Consensus Game: Language Model Generation via Equilibrium Search

arXiv 2310.09139 ↗First posted 13 Oct 2023cs.GT cs.AI cs.CLcited by 35

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Abstract (arXiv)

When applied to question answering and other text generation tasks, language models (LMs) may be queried generatively (by sampling answers from their output distribution) or discriminatively (by using them to score or rank a set of candidate outputs). These procedures sometimes yield very different predictions. How do we reconcile mutually incompatible scoring procedures to obtain coherent LM predictions? We introduce a new, a training-free, game-theoretic procedure for language model decoding. Our approach casts language model decoding as a regularized imperfect-information sequential signaling game - which we term the CONSENSUS GAME - in which a GENERATOR seeks to communicate an abstract correctness parameter using natural language sentences to a DISCRIMINATOR. We develop computational procedures for finding approximate equilibria of this game, resulting in a decoding algorithm we call EQUILIBRIUM-RANKING. Applied to a large number of tasks (including reading comprehension, commonsense reasoning, mathematical problem-solving, and dialog), EQUILIBRIUM-RANKING consistently, and sometimes substantially, improves performance over existing LM decoding procedures - on multiple benchmarks, we observe that applying EQUILIBRIUM-RANKING to LLaMA-7B outperforms the much larger LLaMA-65B and PaLM-540B models. These results highlight the promise of game-theoretic tools for addressing fundamental challenges of truthfulness and consistency in LMs.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). Builds on 40 of its 52 references that are in the map. First posted on arXiv 13 Oct 2023.

Builds on

40 of 52 references.

References · 40

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2022Training language models to follow instructions with human feedbackcited by 15,712
  3. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 13,958
  4. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  5. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  6. 2020Measuring Massive Multitask Language Understandingcited by 7,768
  7. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  8. 2022PaLM: Scaling Language Modeling with Pathwayscited by 5,304
  9. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,710
  10. 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,064
  11. 2023Self-Refine: Iterative Refinement with Self-Feedbackcited by 3,317
  12. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Modelscited by 3,155
28 more
  1. 2021TruthfulQA: Measuring How Models Mimic Human Falsehoodscited by 2,919
  2. 2019The Curious Case of Neural Text Degenerationcited by 2,881
  3. 2022Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language modelscited by 1,970
  4. 2023Improving Factuality and Reasoning in Language Models through Multiagent Debatecited by 1,739
  5. 2022LaMDA: Language Models for Dialog Applicationscited by 1,218
  6. 2018Hierarchical Neural Story Generationcited by 1,182
  7. 2021A General Language Assistant as a Laboratory for Alignmentcited by 1,023
  8. 2023Teaching Large Language Models to Self-Debugcited by 963
  9. 2019How Can We Know What Language Models Know?cited by 953
  10. 2017RACE: Large-scale ReAding Comprehension Dataset From Examinationscited by 851
  11. 2022Contrastive Decoding: Open-ended Text Generation as Optimizationcited by 598
  12. 2022Improving alignment of dialogue agents via targeted human judgementscited by 527
  13. 2023ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMscited by 297
  14. 2023Inverse Scaling: When Bigger Isn't Bettercited by 205
  15. 2023The Capacity for Moral Self-Correction in Large Language Modelscited by 171
  16. 2022Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learningcited by 129
  17. 2022Locally Typical Samplingcited by 108
  18. 2022Language Model Cascadescited by 104
  19. 2021Generate & Rank: A Multi-task Framework for Math Word Problemscited by 82
  20. 2023Contrastive Decoding Improves Reasoning in Large Language Modelscited by 71
  21. 2022Prototypical Calibration for Few-shot Learning of Language Modelscited by 58
  22. 2022A Close Look into the Calibration of Pre-trained Language Modelscited by 57
  23. 2021Modeling Strong and Human-Like Gameplay with KL-Regularized Searchcited by 50
  24. 2022Mastering the Game of No-Press Diplomacy via Human-Regularized Reinforcement Learning and Planningcited by 47
  25. 2022Enhancing Self-Consistency and Performance of Pre-Trained Language Models through Natural Language Inferencecited by 40
  26. 2016Mutual Information and Diverse Decoding Improve Neural Machine Translationcited by 35
  27. 2022On Last-Iterate Convergence Beyond Zero-Sum Gamescited by 30
  28. 2018Online Convex Optimization for Sequential Decision Processes and Extensive-Form Gamescited by 21

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 10; 2025: 16; 2026: 7.

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  2. 2024PrivacyLens: Evaluating Privacy Norm Awareness of Language Models in Actioncited by 161
  3. 2024Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systemscited by 94
  4. 2025Multiagent Finetuning: Self Improvement with Diverse Reasoning Chainscited by 90
  5. 2024Learning How Hard to Think: Input-Adaptive Allocation of LM Computationcited by 67
  6. 2024Internal Consistency and Self-Feedback in Large Language Models: A Surveycited by 49
  7. 2024A Language Model's Guide Through Latent Spacecited by 43
  8. 2025Privacy in Action: Towards Realistic Privacy Mitigation and Evaluation for LLM-Powered Agentscited by 33
  9. 2025Amulet: ReAlignment During Test Time for Personalized Preference Adaptation of LLMscited by 29
  10. 2024Steering Language Models with Game-Theoretic Solverscited by 28
  11. 2025A Survey on LLM Test-Time Compute via Search: Tasks, LLM Profiling, Search Algorithms, and Relevant Frameworkscited by 21
  12. 2025Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontierscited by 14
23 more
  1. 2025Instance-Dependent Regret Bounds for Learning Two-Player Zero-Sum Games with Bandit Feedbackcited by 9
  2. 2025Incentivizing Truthful Language Models via Peer Elicitation Gamescited by 8
  3. 2024Self-Consistency Falls Short! The Adverse Effects of Positional Bias on Long-Context Problemscited by 7
  4. 2025Position: Towards a Responsible LLM-empowered Multi-Agent Systemscited by 7
  5. 2025Stop Reducing Responsibility in LLM-Powered Multi-Agent Systems to Local Alignmentcited by 7
  6. 2024Decoding Game: On Minimax Optimality of Heuristic Text Generation Strategiescited by 6
  7. 2024Engagement-Driven Content Generation with Large Language Modelscited by 5
  8. 2025Multiplayer Federated Learning: Reaching Equilibrium with Less Communicationcited by 5
  9. 2023Regularized Conventions: Equilibrium Computation as a Model of Pragmatic Reasoningcited by 4
  10. 2024Truth or Deceit? A Bayesian Decoding Game Enhances Consistency and Reliabilitycited by 2
  11. 2025Utility-inspired Reward Transformations Improve Reinforcement Learning Training of Language Modelscited by 2
  12. 2025On Separation Between Best-Iterate, Random-Iterate, and Last-Iterate Convergence of Learning in Gamescited by 2
  13. 2025A Game-Theoretic Negotiation Framework for Cross-Cultural Consensus in LLMscited by 2
  14. 2025Reranking-based Generation for Unbiased Perspective Summarizationcited by 2
  15. 2026ALIGN: Aligned Delegation with Performance Guarantees for Multi-Agent LLM Reasoningcited by 2
  16. 2026LinguaGame: A Linguistically Grounded Game-Theoretic Paradigm for Multi-Agent Dialogue Generationcited by 1
  17. 2026Power and Limitations of Aggregation in Compound AI Systemscited by 1
  18. 2026HCAG: Hierarchical Abstraction and Retrieval-Augmented Generation on Theoretical Repositories with LLMscited by 1
  19. 2025Transparent Visual Reasoning via Object-Centric Agent Collaborationcited by 0
  20. 2025Safety Game: Inference-Time Alignment of Black-Box LLMs via Constrained Optimizationcited by 0
  21. 2026Agent-based imitation dynamics can yield efficiently compressed population-level vocabulariescited by 0
  22. 2026Wasserstein Equilibrium Decoding for Reliable Medical Visual Question Answeringcited by 0
  23. 2026Is Lying an Emergent Behaviour in LLMs? Evidence from Gaslighting AI agents in a Sustainability Gamecited by 0

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  8. 2025SKATE, a Scalable Tournament Eval: Weaker LLMs differentiate between stronger ones using verifiable challenges