Game theory is the study of mathematical models of strategic interactions among rational agents. Language is a key medium of interaction for humans, though it has historically proven difficult to model dialogue and its strategic motivations mathematically. A suitable model of the players, strategies, and payoffs associated with linguistic interactions (i.e., a binding to the conventional symbolic logic of game theory) would enable existing game-theoretic algorithms to provide strategic solutions in the space of language. In other words, a binding could provide a route to computing stable, rational conversational strategies in dialogue. Large language models (LLMs) have arguably reached a point where their generative capabilities can enable realistic, human-like simulations of natural dialogue. By prompting them in various ways, we can steer their responses towards different output utterances. Leveraging the expressivity of natural language, LLMs can also help us quickly generate new dialogue scenarios, which are grounded in real world applications. In this work, we present one possible binding from dialogue to game theory as well as generalizations of existing equilibrium finding algorithms to this setting. In addition, by exploiting LLMs generation capabilities along with our proposed binding, we can synthesize a large repository of formally-defined games in which one can study and test game-theoretic solution concepts. We also demonstrate how one can combine LLM-driven game generation, game-theoretic solvers, and imitation learning to construct a process for improving the strategic capabilities of LLMs.

翻译：博弈论是研究理性主体间策略互动的数学模型。语言是人类互动的关键媒介，但历史上难以用数学方法对对话及其战略动机进行建模。为语言互动中的参与者、策略和收益建立适当模型（即与博弈论传统符号逻辑的绑定），将使现有博弈论算法能在语言空间中提供战略解。换言之，这种绑定可提供一条在对话中计算稳定、理性的会话策略的途径。大型语言模型（LLM）的生成能力已足以实现逼真且类人的自然对话模拟。通过不同方式的提示，我们可以引导其输出至不同的表述。借助自然语言的表达力，LLM还能快速生成基于现实应用的新型对话场景。本研究提出一种从对话到博弈论的可行绑定方法，并推广了现有均衡求解算法以适配该场景。此外，利用LLM的生成能力与所提绑定，我们可合成包含大量形式化定义的游戏库，用于研究与检验博弈论解概念。我们同时展示了如何结合LLM驱动的游戏生成、博弈论求解器与模仿学习，构建提升LLM战略能力的优化流程。