  As large language models (LLMs) start interacting with each other and
generating an increasing amount of text online, it becomes crucial to better
understand how information is transformed as it passes from one LLM to the
next. While significant research has examined individual LLM behaviors,
existing studies have largely overlooked the collective behaviors and
information distortions arising from iterated LLM interactions. Small biases,
negligible at the single output level, risk being amplified in iterated
interactions, potentially leading the content to evolve towards attractor
states. In a series of telephone game experiments, we apply a transmission
chain design borrowed from the human cultural evolution literature: LLM agents
iteratively receive, produce, and transmit texts from the previous to the next
agent in the chain. By tracking the evolution of text toxicity, positivity,
difficulty, and length across transmission chains, we uncover the existence of
biases and attractors, and study their dependence on the initial text, the
instructions, language model, and model size. For instance, we find that more
open-ended instructions lead to stronger attraction effects compared to more
constrained tasks. We also find that different text properties display
different sensitivity to attraction effects, with toxicity leading to stronger
attractors than length. These findings highlight the importance of accounting
for multi-step transmission dynamics and represent a first step towards a more
comprehensive understanding of LLM cultural dynamics.
