Exploring the Topology and Memory of Consensus: How LLM Agents Agree, Fragment, or Settle When Forming Conventions
For researchers designing LLM-based multi-agent systems, the paper demonstrates that memory and topology must be co-designed, as optimizing them independently can lead to opposite effects on coordination outcomes.
The paper shows that memory depth and network topology interact to reverse the effect of memory on consensus speed in LLM multi-agent systems, with longer memory slowing decentralized networks but accelerating centralized ones, while centralized networks lock into fragmented plateaus faster. Across 432 simulations, a memory-mediated speed-unity trade-off is documented, and agent behavior is best modeled by belief-based (Fictitious Play) rather than reward-based adaptation.
How much should an LLM agent remember, and how should multi-agent systems be connected when trying to reach consensus? We show these two design choices interact in a way that flips the sign of memory's effect on coordination. Across 432 simulation runs of a networked Naming Game on eight fixed 16-agent topologies, we vary memory depth and network structure. Longer memory slows the time to reach steady state in decentralized networks but accelerates it in centralized ones; the same parameter pushes the system in opposite directions depending on topology. Critically, "faster settling" in centralized networks means locking in to a fragmented plateau more quickly, not reaching system-wide consensus, which can be used to generate diverging opinions. We further document a memory-mediated speed-unity trade-off: centralized networks consistently preserve more competing conventions than decentralized networks, but their settling speed depends sharply on memory. At the agent level, within-network analyses show that high-betweenness bridges suffer a brokerage penalty while agents in locally clustered neighborhoods achieve higher coordination success. Finally, in search of analytically tractable generative mechanisms, we find that agents' choices are well captured by Fictitious Play, indicating belief-based rather than reward-based adaptation. The practical implication: memory depth and communication topology should be co-designed, not optimized in isolation.