Collaborative Spatial Learning with Multi-LLM Agents in Networked Social Experiments¶

🕒 Published (v1): 2026-07-16 05:11 UTC · Source: Arxiv · link

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Multi-LLM agents in networked experiments; exploit/explore tradeoff across agent collectives

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TL;DR¶

This paper replicates the Mason–Watts networked collective-search experiment (PNAS 2012) using groups of 16 LLM agents across eight network topologies, finding that LLMs reproduce the human network-efficiency effect only when given a single-sentence randomization instruction at initialization. Bayesian optimization agents using Gaussian processes outperform all LLM variants on this spatial search task.

Problem¶

It is unknown whether communication network topology affects collective performance of LLM multi-agent systems, and whether LLMs replicate the human finding that shorter-path networks produce higher cumulative payoffs on spatial search tasks. Prior work on LLM exploration–exploitation uses single-agent bandit settings without varying network structure or comparing against mechanistic baselines.

Method¶

Groups of $N=16$ independent LLM agent instances (OpenAI gpt-oss-120b, 117B-parameter MoE, medium reasoning-effort) play the Wildcat Wells game: sequentially choosing cells on a discrete $101\times101$ grid for $T=15$ rounds, maximizing cumulative payoff $\bar{f}_{\text{cum}} = \frac{1}{NT}\sum_i\sum_t f(x_i^{(t)})$. Each agent observes its own history and the full histories of its three network neighbors. The experiment crosses: - 4 agent types: LLM (default), LLM-RI (random initialization — one added sentence instructs uniform first-round sampling), EI (Expected Improvement GP-BO), UCB (Upper Confidence Bound GP-BO) - 8 network topologies: the original Mason–Watts 3-regular graphs on 16 nodes, APL ranging from 2.20 to 3.87 - 3 landscape complexity levels (0, 3, or 8 secondary peaks), 20 replicates each

The GP surrogate for Bayesian agents uses an additive RBF kernel $k = k_{\text{short}} + k_{\text{long}}$ fitted to the agent's own and neighbors' observations; acquisition functions are: $$\alpha_{\text{EI}}(x) = (\mu(x)-f^*)\Phi(z) + \sigma(x)\phi(z), \quad z = \frac{\mu(x)-f^*}{\sigma(x)}$$ $$\alpha_{\text{UCB}}(x) = \mu(x) + \kappa_t \sigma(x)$$ Total: 2,400 games and 576,000 node-round observations. Human data from 232 original Mason–Watts sessions serve as an unmatched behavioral reference.

Key Contributions¶

First systematic experiment placing groups of LLM agents on all eight Mason–Watts network topologies for sequential spatial search
A reproducible bank of 60 two-dimensional fitness landscapes at three complexity levels (Perlin-noise + Gaussian peaks, deterministic seeding)
Bayesian optimization (EI, UCB) agents that consume the same neighbor observations as LLMs, serving as mechanistic performance ceilings
Empirical finding that a single-sentence prompt change (randomization instruction) produces a collective payoff improvement more than 3× the range of the network-topology effect

Results¶

Agent performance ranking (final-round group-mean payoff): UCB/EI at 97–100 > LLM-RI at 93–97 > LLM (default) at 84–91 >> Random baseline at 39–47
Near-peak discovery rate by round 15: UCB/EI 91–99% of games; LLM-RI 62–76%; default LLM only 25–54%
Network-efficiency effect (OLS of cumulative payoff on APL, negative $\beta$ = shorter path → higher payoff):
LLM-RI: $\hat\beta=-1.37$, $p=0.003$ (game-level); $p=0.003$ (graph-level) ✓
EI: $\hat\beta=-0.99$, $p=0.026$ / $p<0.001$ ✓
UCB: $\hat\beta=-1.26$, $p=0.005$ / $p<0.001$ ✓
Default LLM: $\hat\beta=-0.41$, $p=0.619$ / $p=0.260$ — no significant effect
Human reference: $\hat\beta=-4.65$, $p=0.010$ (game-level)
The randomization instruction alone improves collective payoff by more than 3× the payoff spread across the eight topologies
Default LLM agents exhibit center-start clustering: nearly all first-round choices cluster near (50, 50), suppressing diversity and preventing the network topology from having a detectable effect
LLM copying behavior is largely positional (copying neighbor coordinates regardless of payoff level) rather than payoff-conditional, unlike human participants

Limitations¶

Only one LLM family/model tested (gpt-oss-120b); results are explicitly version-dependent and may not generalize across model generations
Human data come from different landscape instances (not publicly available), precluding absolute payoff comparisons
Network topologies restricted to the eight original Mason–Watts 3-regular graphs; random or other topologies not explored
Agents are stateless per round (no within-game memory beyond the structured prompt context); this is an architectural constraint, not a study of memory mechanisms
The paper is truncated; results on spatial diversity, copying analysis, and ablations beyond what is shown may be incomplete in the provided text

Relevance to Agentic AI / LLM Agents¶

This work provides the first controlled empirical study of how communication network structure modulates collective performance in LLM multi-agent systems, directly connecting the multi-agent LLM literature to the social-science literature on networked collective intelligence. The finding that a single-sentence prompt intervention (forcing first-round diversity) unlocks the network-efficiency effect — producing gains larger than the entire topology effect — has direct implications for prompt engineering in collaborative LLM deployments. The comparison against Gaussian-process Bayesian optimization baselines quantifies LLMs' exploration–exploitation shortfall on a well-defined spatial task, offering a concrete behavioral benchmark for agentic system designers. The result that LLM copying is positional rather than payoff-conditional distinguishes LLM social learning from human adaptive strategies and flags a systematic behavioral bias relevant to any multi-agent system relying on peer imitation.