The Butterfly Defects: Tracing Cooperation in LLM Agent Networks

Abstract

As large language models (LLMs) increasingly operate as interconnected agents, a fundamental question emerges: does individual cooperation translate into collective cooperation? We investigate this question through the Iterated Prisoner's Dilemma (IPD), moving from dyadic interactions to homogeneous and heterogeneous networks of open-weight LLMs. Our findings reveal that cooperation is highly sensitive to model composition and seemingly minor linguistic changes. Models that cooperate with identical peers can shift toward defection in mixed populations. A simple uncertainty cue can increase or decrease cooperation, redistribute costs, and affect unexposed agents several hops away. Even reversing action-label order can dramatically alter behavior, with uncertainty framing sometimes amplifying this sensitivity. Together, these findings challenge the notion of cooperation as a stable model-level property, revealing how strategic behavior depends on interaction partners, network positions, and the language used to frame decisions.