Language Games, Game Theory, and Large Language Models: A Mathematical Framework

Abstract

Language is a fundamental tool for communication and reasoning, yet its strategic use in various contexts can be modeled as a game. In this paper, we connect the philosophical concept of language games with gametheoretic models and the computational functionality of large language models (LLMs). We explore how LLMs participate in language games, propose mathematical models for interaction between agents using game theory, and investigate how strategic communication can emerge in multiagent systems. By extending traditional game-theoretic frameworks such as sender-receiver games and cheap talk, we formalize the strategic use of language in LLMs. We also discuss recent works on multi-agent systems and strategic communication in computational linguistics and present key challenges in implementing these frameworks with current LLM architectures.

Keywords: artificial intelligence, language models, communication, game theory

JEL Classification: C70, C73, D83, C72, O30, I20