  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.
