Title: Investigating Consensus Dynamics: The Interplay of Network Topology and Agent Memory in Convention Formation

Abstract:

This study examines the critical design decisions regarding how much an LLM agent should retain and how multi-agent systems should be structured to achieve agreement. We demonstrate that these two factors interact in a manner that reverses the impact of memory on coordination. Through 432 simulation runs of a networked Naming Game across eight fixed topologies involving 16 agents, we manipulated both network structure and memory depth. Our findings reveal that while extended memory delays the attainment of steady state in decentralized networks, it hastens this process in centralized ones; essentially, the same parameter drives the system in opposing directions based on its topology. Notably, the accelerated convergence observed in centralized networks does not necessarily equate to achieving system-wide consensus. Instead, it often results in the rapid establishment of fragmented plateaus, a phenomenon that can be leveraged to cultivate diverging viewpoints.

We further identify a trade-off mediated by memory between speed and unity. Centralized networks tend to maintain a greater number of competing conventions compared to their decentralized counterparts, yet their rate of settling is highly sensitive to memory depth. At the individual agent level, analyses within networks indicate that agents occupying high-betweenness bridge positions incur a brokerage penalty, whereas those situated in locally clustered neighborhoods experience higher success rates in coordination. Finally, seeking an analytically manageable generative mechanism, we found that agent choices are accurately modeled by Fictitious Play, suggesting that adaptation is belief-based rather than reward-based. The key practical takeaway is that memory depth and communication topology must be co-designed, rather than optimized independently.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC