LLM agent consensus study reveals memory-topology trade-off

A new study from Aliakbar Mehdizadeh and Martin Hilbert, submitted to the Journal of Artificial Societies and Social Simulation, explores how LLM agents reach consensus in multi-agent systems. Using a networked Naming Game with 16 agents across eight fixed topologies, the researchers ran 432 simulation runs to vary memory depth and network structure. They discovered that the effect of memory flips depending on topology: longer memory slows convergence in decentralized networks but accelerates it in centralized ones. However, that faster settling in centralized networks often leads to a fragmented plateau—multiple competing conventions instead of system-wide agreement. This means the same memory parameter can push the system toward opposite outcomes based solely on how agents are connected.

The study also documents a memory-mediated speed-unity trade-off: centralized networks preserve more competing conventions overall, but their settling speed is sharply influenced by memory depth. At the agent level, high-betweenness nodes (bridges) suffer a brokerage penalty—they coordinate less successfully—while agents in locally clustered neighborhoods achieve higher coordination. The researchers found that agents' choices are well captured by Fictitious Play, a belief-based adaptation model, rather than reward-based learning. The practical takeaway is clear: memory depth and communication topology should be co-designed as a system, not optimized in isolation. For engineers building multi-agent LLM systems, this work shows that simply increasing memory or choosing a network structure without considering their interaction can lead to unintended fragmentation or slowdown.