Abstract
Text revision has become an integral component of large language models. This paper formulates revision such that it admits a Nash equilibrium: Token positions are players, vocabulary items are actions, and each player's utility is the language model's log conditional probability. We motivate the revision by showing that Nash equilibria can have exponentially higher likelihood than autoregressive outputs as the sequence length grows. We further propose Nash decoding, an algorithm that reaches an $\varepsilon$-Nash equilibrium in $O(1/\varepsilon)$ time given access to the joint probability of tokens conditioned on a prompt. In practice, we run Nash decoding using conditional probability estimates from large language models and evaluate the resulting equilibria on question-answering benchmarks. On CLAPNQ, PubMedQA, and CoQA, Nash equilibria obtained from masked language models achieve higher F1 and ROUGE scores than autoregressive models up to $18\times$ larger, without any fine-tuning or retraining, at the cost of additional test-time computation.
Keywords
Publication details
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Cite this article
APA 7
Jafari, A., Adibi, A., Ghavamzadeh, M., & Daneshmand, H. (2026). Nash Equilibrium Text: A Game-Theoretic Decoding Framework for Text Generation. https://omanscience.com/en/articles/nash-equilibrium-text-a-game-theoretic-decoding-framework-for-text-generation
MLA 9
Jafari, Alireza, et al. "Nash Equilibrium Text: A Game-Theoretic Decoding Framework for Text Generation." https://omanscience.com/en/articles/nash-equilibrium-text-a-game-theoretic-decoding-framework-for-text-generation.
Chicago (author–date)
Jafari, Alireza, Arman Adibi, Mohammad Ghavamzadeh, and Hadi Daneshmand. 2026. "Nash Equilibrium Text: A Game-Theoretic Decoding Framework for Text Generation." https://omanscience.com/en/articles/nash-equilibrium-text-a-game-theoretic-decoding-framework-for-text-generation.
Harvard
Jafari, A., Adibi, A., Ghavamzadeh, M. and Daneshmand, H. (2026) 'Nash Equilibrium Text: A Game-Theoretic Decoding Framework for Text Generation', Available at: https://omanscience.com/en/articles/nash-equilibrium-text-a-game-theoretic-decoding-framework-for-text-generation.
Vancouver
Jafari A, Adibi A, Ghavamzadeh M, Daneshmand H. Nash Equilibrium Text: A Game-Theoretic Decoding Framework for Text Generation. https://omanscience.com/en/articles/nash-equilibrium-text-a-game-theoretic-decoding-framework-for-text-generation
IEEE
A. Jafari, A. Adibi, M. Ghavamzadeh, and H. Daneshmand, "Nash Equilibrium Text: A Game-Theoretic Decoding Framework for Text Generation," https://omanscience.com/en/articles/nash-equilibrium-text-a-game-theoretic-decoding-framework-for-text-generation.