Strategic Interactions between Large Language Models-based Agents in Beauty Contests

TL;DR

This paper investigates how large language model-based agents behave in a classical beauty contest game, revealing their strategic reasoning levels, convergence patterns to Nash Equilibrium, and effects of environment composition on outcomes.

Contribution

It provides the first analysis of multi-agent LLM interactions in a game-theoretic setting, highlighting their reasoning levels, convergence behavior, and impact of environment composition.

Findings

LLM agents show reasoning levels between 0 and 1, lower than humans.

Agents tend to converge towards Nash Equilibrium in repeated games.

Mixed environments with diverse agent levels accelerate convergence.

Abstract

The growing adoption of large language models (LLMs) presents potential for deeper understanding of human behaviours within game theory frameworks. Addressing research gap on multi-player competitive games, this paper examines the strategic interactions among multiple types of LLM-based agents in a classical beauty contest game. LLM-based agents demonstrate varying depth of reasoning that fall within a range of level-0 to 1, which are lower than experimental results conducted with human subjects, but they do display similar convergence pattern towards Nash Equilibrium (NE) choice in repeated setting. Further, through variation in group composition of agent types, I found environment with lower strategic uncertainty enhances convergence for LLM-based agents, and having a mixed environment comprises of LLM-based agents of differing strategic levels accelerates convergence for all. Higher average payoffs for the more intelligent agents are usually observed, albeit at the expense of less intelligent agents. The results from game play with simulated agents not only convey insights on potential human behaviours under specified experimental set-ups, they also offer valuable understanding of strategic interactions among algorithms.