Multi-Agent Consensus Seeking via Large Language Models

Topic and motivation

• Consensus seeking is studied as multiple LLM-driven agents continuously negotiating initially different numerical states until they reach a common final state.The task abstracts more complex agent states, such as thoughts, objectives, or solutions.Source: §1 · pp. 1–2

Consensus strategy

• When no strategy is prescribed, agents primarily use an average strategy, setting each next state to the average of current agent states.They occasionally use other strategies, and this behavior resembles average consensus studied in cooperative control.Source: §1 · p. 2

Impact of personality

• Stubborn agents dominate the final consensus value, producing a leader-follower structure relative to more changeable suggestible agents.Personality therefore affects both negotiation behavior and the resulting group outcome.Source: §1 · p. 2

Impact of topology

• Fully connected networks converge fastest, whereas incomplete networks slow convergence; directed graphs can create leader-follower outcomes or clustering.The consensus process is jointly shaped by topology and personality.Source: §1 · p. 2

Impact of agent number

• As the agent count increases, final-consensus variance decreases and larger groups can suppress state oscillations among suggestible agents.These results suggest that more agents can reduce randomness or hallucinations and stabilize group decision-making.Source: §1 · p. 2

Application to multi-robot aggregation

• Applied to multi-robot aggregation, the framework coordinates robots from different initial positions toward a common planar position and demonstrates potential for zero-shot autonomous planning.The application treats consensus seeking as cooperative planning based on simple verbal commands.Source: §1 · p. 2

Problem setup

• Each GPT-3.5-turbo-0613 agent starts with a random state between 0 and 100, then negotiates across rounds toward a shared consensus value.The state can represent a one-dimensional position or an index for a more complex solution space.Source: §2 · p. 4

Negotiation process

• In every round, each agent uses the other agents’ states to choose a new state, outputting both reasoning and a position.The reasoning component helps guide reliable answers and exposes the strategy used.Source: §2 · p. 4

State interpretation

• The numerical state abstracts thoughts, objectives, solutions, or robot positions, making consensus analogous to multi-robot aggregation.For robots, aggregation means converging from different locations to the same location.Source: §2 · p. 4

Autonomous strategy selection

• Agents are not directly instructed which consensus strategy to adopt so they can autonomously generate strategies for more complex tasks.This design avoids relying on strategies that may be unknown in harder problem settings.Source: §2 · p. 4

3.1 Consensus strategies and consensus values

• Most experiments reached consensus, with agents commonly adopting an average strategy, though suggestable, stubborn, and erroneous strategies sometimes caused oscillation, compromise, or propagated mistakes.The average strategy sets each next state to the average of current states; agents may exclude their own state.Source: §3.1 · pp. 4, 6
• The final consensus value was usually close to the initial-state average, while larger agent groups reduced variance and lower temperature produced slightly tighter concentration around that average.The Monte Carlo study used 2,400 experiments across 2, 4, 6, and 8 agents and temperatures 0.0 and 0.7.Source: §3.1 · p. 6, Figure 4 · p. 6

3.2 Impact of personality

• With two agents, one stubborn and one suggestible agent converged toward the stubborn agent, whereas two suggestible agents could oscillate and two stubborn agents converged slowly or not at all.These outcomes show that personality changes both the negotiation path and the difficulty of reaching consensus.Source: §3.2 · p. 8
• With ten agents, suggestible agents often reached consensus without oscillation, but multiple stubborn agents could form separate clusters and create a deadlock.The larger group tended to choose states where the majority resided, suppressing oscillations among suggestible agents.Source: §3.2 · p. 8

3.3 Impact of network topology

• In undirected networks, full connectivity produced fast convergence, while incomplete connectivity still allowed consensus but slowed it.In the incomplete topology, agents 2 and 3 could not exchange information directly.Source: §3.3 · p. 9, Figure 8 · p. 9
• Directed networks produced leader-follower consensus: downstream agents converged toward the leader’s state, with longer information paths slowing convergence.The leader could not receive information from followers, so its state determined the final outcome.Source: §3.3 · p. 10, Figure 9 · p. 10
• The negotiation process is jointly shaped by topology and personality, while communication delays and agent-weight assignments remain additional factors that may affect consensus.These factors define important boundaries for interpreting the reported experiments.Source: §3.3 · pp. 10–11

• Robots starting from different initial positions eventually converge to the same position in the two-dimensional plane.Source: §4 · p. 11
• The LLM planner outputs discontinuous target states, while the controller effectively tracks those targets.Source: §4 · p. 11
• Each robot combines an LLM-driven planner, which outputs target states from other robots’ current states, with a controller that generates velocity commands.Source: §4 · p. 11
• The simulation uses two-dimensional prompts, undefined robot personalities, and a fully connected inter-robot communication topology.Source: §4 · p. 11

• Prior LLM multi-agent systems decompose complex tasks into subtasks handled by agents according to expertise, reducing hallucination risk.Source: §5 · p. 11
• Other systems use continuous debates in which agents correct misconceptions through interaction until consensus is reached.Source: §5 · p. 11
• Research has simulated human bargaining, strategic games, sandbox games, social interactions, humanoid agents, and classic game-theory settings.Source: §5 · p. 11
• Although prior work examines individual-LLM non-selfconsistency and consensus among different LLM types, consensus seeking itself and its influencing factors remain insufficiently addressed.Source: §5 · p. 11

• LLM-driven agents primarily use the average strategy, and consensus outcomes are jointly affected by agent personality and network topology.Source: §6 · p. 12
• Increasing the number of agents can alleviate system hallucinations and may stabilize group decision-making.Source: §6 · p. 12
• These findings can potentially provide foundations for understanding LLM-driven multi-agent systems solving more complex collaborative tasks.Source: §6 · p. 13
• The study uses numerical agent states, evaluates only ChatGPT 3.5, and applies a low-update-rate planner in multi-robot tasks, limiting generalization and high-performance use.Source: §6 · p. 13

• The procedure extracts new locations from agent responses, updates the state, records conversation contexts, and stores the experiment data.Source: §A.1 · p. 16
• The procedure initializes agents, a connectivity matrix, personalities, random locations, experiment records, and round contexts.Source: §A.1 · p. 16
• For each round, every agent receives its own location and the locations of agents connected through the communication matrix.Source: §A.1 · p. 16
• Prompts define agents as moving in one-dimensional space and optionally assign stubborn or suggestible personalities.Source: §A.1 · p. 16
• Initial prompts ask agents to choose positions for gathering with one or multiple other agents and briefly explain their decisions.Source: §A.1 · p. 16
• After each round, prompts ask agents to select their next position using their updated location and other agents’ latest positions.Source: §A.1 · pp. 16–17

• Agents may misunderstand their personalities because of hallucination, sometimes acting against their inherent personalities during gathering.Source: §A.2 · p. 17
• A stubborn agent may stay at position 9.0 rather than adopt another agent’s position of 44.0 because the latter is farther from the gathering point.Source: §A.2 · p. 17
• With two suggestible agents, both may nevertheless remain stationary in a special aggregation scenario.Source: Figure 11 · p. 17