Exploring the Topology and Memory of Consensus: How LLM Agents Agree, Fragment, or Settle When Forming Conventions
2026-06-02 • Multiagent Systems
Multiagent SystemsComputation and LanguageSocial and Information Networks
AI summaryⓘ
The authors studied how much memory large language model agents should have and how their communication networks should be set up to agree on something. They found that the effect of memory on reaching agreement depends on the network structure: in decentralized networks, more memory slows things down, while in centralized ones, it speeds things up—but this speed-up can trap the system in divided opinions instead of full agreement. They also showed that agents with important network roles face challenges, and that agents seem to learn by updating their beliefs rather than just chasing rewards. Overall, the authors suggest designing memory and communication patterns together for better coordination.
Large Language Model (LLM) agentsNaming Gamememory depthnetwork topologycentralized vs decentralized networksconsensus reachingbetweenness centralityFictitious Playmulti-agent systemscoordination dynamics
Authors
Aliakbar Mehdizadeh, Martin Hilbert
Abstract
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.