Game-theoretic LLM: Agent Workflow for Negotiation Games
Authors: name: Wenyue Hua, name: Ollie Liu, name: Lingyao Li, name: Alfonso Amayuelas, name: Julie Chen, name: Lucas Jiang, name: Mingyu Jin, name: Lizhou Fan, name: Fei Sun, name: William Wang, name: Xintong Wang, name: Yongfeng Zhang

This paper investigates the rationality of large language models (LLMs) in
strategic decision-making contexts, specifically within the framework of game
theory. We evaluate several state-of-the-art LLMs across a spectrum of
complete-information and incomplete-information games. Our findings reveal that
LLMs frequently deviate from rational strategies, particularly as the
complexity of the game increases with larger payoff matrices or deeper
sequential trees.
  To address these limitations, we design multiple game-theoretic workflows
that guide the reasoning and decision-making processes of LLMs. These workflows
aim to enhance the models' ability to compute Nash Equilibria and make rational
choices, even under conditions of uncertainty and incomplete information.
Experimental results demonstrate that the adoption of these workflows
significantly improves the rationality and robustness of LLMs in game-theoretic
tasks. Specifically, with the workflow, LLMs exhibit marked improvements in
identifying optimal strategies, achieving near-optimal allocations in
negotiation scenarios, and reducing susceptibility to exploitation during
negotiations. Furthermore, we explore the meta-strategic considerations of
whether it is rational for agents to adopt such workflows, recognizing that the
decision to use or forgo the workflow constitutes a game-theoretic issue in
itself.
  Our research contributes to a deeper understanding of LLMs' decision-making
capabilities in strategic contexts and provides insights into enhancing their
rationality through structured workflows. The findings have implications for
the development of more robust and strategically sound AI agents capable of
navigating complex interactive environments. Code and data supporting this
study are available at https://github.com/Wenyueh/game_theory.