# Exploring the Topology and Memory of Consensus: How LLM Agents Agree, Fragment, or Settle When Forming Conventions

arXiv: https://arxiv.org/abs/2606.04197 · HTML: https://mlsanity.com/paper/2606.04197/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 28 of its 79 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 28 of 28)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [Mind2Web: Towards a Generalist Agent for the Web](https://mlsanity.com/paper/2306.06070/) (2023)
- [A Survey on the Memory Mechanism of Large Language Model based Agents](https://mlsanity.com/paper/2404.13501/) (2024)
- [Multi-Agent Collaboration Mechanisms: A Survey of LLMs](https://mlsanity.com/paper/2501.06322/) (2025)
- [Fully Decentralized Multi-Agent Reinforcement Learning with Networked Agents](https://mlsanity.com/paper/1802.08757/) (2018)
- [Towards a Science of Scaling Agent Systems](https://mlsanity.com/paper/2512.08296/) (2025)
- [Emergent social conventions and collective bias in LLM populations](https://mlsanity.com/paper/2410.08948/) (2024)
- [How Memory Management Impacts LLM Agents: An Empirical Study of Experience-Following Behavior](https://mlsanity.com/paper/2505.16067/) (2025)
- [MemInsight: Autonomous Memory Augmentation for LLM Agents](https://mlsanity.com/paper/2503.21760/) (2025)
- [Machine Culture](https://mlsanity.com/paper/2311.11388/) (2023)
- ["Humans welcome to observe": A First Look at the Agent Social Network Moltbook](https://mlsanity.com/paper/2602.10127/) (2026)
- [The Spontaneous Emergence of Conventions: An Experimental Study of Cultural Evolution](https://mlsanity.com/paper/1502.06910/) (2015)
- [When Your AI Agent Succumbs to Peer-Pressure: Studying Opinion-Change Dynamics of LLMs](https://mlsanity.com/paper/2510.19107/) (2025)
- [Exploring Silicon-Based Societies: An Early Study of the Moltbook Agent Community](https://mlsanity.com/paper/2602.02613/) (2026)
- [The Emergence of Consensus: A Primer](https://mlsanity.com/paper/1704.07767/) (2017)
- [Learning How to Remember: A Meta-Cognitive Management Method for Structured and Transferable Agent Memory](https://mlsanity.com/paper/2601.07470/) (2026)
- [Homophily-induced Emergence of Biased Structures in LLM-based Multi-Agent AI Systems](https://mlsanity.com/paper/2510.02637/) (2025)
- [Gender Dynamics and Homophily in a Social Network of LLM Agents](https://mlsanity.com/paper/2602.02606/) (2026)
- [Towards Pervasive Distributed Agentic Generative AI -- A State of The Art](https://mlsanity.com/paper/2506.13324/) (2025)
- [Analyzing Character and Consciousness in AI-Generated Social Content: A Case Study of Chirper, the AI Social Network](https://mlsanity.com/paper/2309.08614/) (2023)
- [Epistemic Substitution: How Grokipedia's AI-Generated Encyclopedia Restructures Authority](https://mlsanity.com/paper/2512.03337/) (2025)

## Built on by (most cited first, 3 of 3)

- [Microscopic dynamics of consensus formation in multi-agent LLM Naming Games](https://mlsanity.com/paper/2608.02178/) (2026)
- [One Axis, No Brake: Self-Knowledge Limits the Filtering of Harmful Peer Conformity in LLMs](https://mlsanity.com/paper/2609.18998/) (2026)
- [Drivers of LLM Consensus Formation Under Competing Incentives: A Simulation Study](https://mlsanity.com/paper/2610.20200/) (2026)

## Abstract (arXiv)

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.