Information Limits and Attractor Dynamics in Economies of Frontier LLM Agents: A Pre-Registered Test
Quick Answer
This paper shows that A pre-registered experiment on Claude Opus 4.8 investigates wealth growth and population misalignment in multi-agent economies, revealing that relative growth aligns with claimed information but fails to demonstrate expected noise-maintained dispersion.
Quick Take
The experiment cost $138.76 and is fully reproducible from cached outputs.
Key Points
- Confirmed that relative growth in coupled economies equals claimed information with a maximum gap of 46 millinats.
- Coalition value is submodular under conditional independence, flipping to supermodular with XOR synergy control.
- Residual-scaling test failed, showing goal dispersion collapsed across all population runs.
- No population achieved the noise-maintained dispersion assumed by the smooth mean-field model.
- Experiment protocol, pre-registration chain, and analysis code are publicly available.
DeepSignal Analysis
What happened
A pre-registered experiment using Claude Opus 4.8 tested wealth growth and population dynamics in multi-agent economies. The first result confirmed that relative growth aligns with claimed information, while the second result indicated a failure to achieve expected noise-maintained dispersion, with goal dispersion collapsing across all runs.
Key evidence
- The experiment cost $138.76 and is reproducible from cached outputs, ensuring transparency and accessibility.
- In the first result, the gap law held with a maximum deviation of 46 millinats, confirming the relationship between relative growth and claimed information.
- The second result showed that no tested LLM population achieved the noise-maintained-dispersion regime, with goal dispersion collapsing to a maximum of 4.85 against a frozen floor of 5.31.
Why it matters
This study provides insights into the dynamics of multi-agent systems using advanced language models, highlighting both the potential for wealth growth and the limitations in achieving expected population behaviors. The findings challenge assumptions about agent interactions and information processing in economic models, which could influence future research and applications in AI-driven economies.
Paper Resources
📖 Reader Mode
~2 min readAbstract:We report a pre-registered, two-part experiment on small economies of frontier language-model agents (Claude Opus 4.8), testing two quantitative predictions about coupled multi-agent systems: an information-theoretic capacity region for wealth growth under market coupling, and a mean-field residual-scaling law for population misalignment under incentive and control levers. All predictions, acceptance bands, and decision rules were frozen in a public git chain before any run; every reported number re-derives mechanically from cached model outputs; the entire experiment cost $138.76 in metered API spend and is re-runnable at zero cost from the cache.
Result 1 (confirmation): in parimutuel-coupled economies, relative growth equals relative claimed information -- the gap law G_a - G_b = I_a - I_b holds to a worst-case 46 millinats (pre-registered band: 50) across four perception structures; coalition value is submodular exactly where channels are conditionally independent, and a designed XOR synergy control flips it supermodular by 0.62 >= ln2/2 nats, with agents reasoning out the joint bit; the joint growth ceiling G_S <= H(X) binds exactly; and the best-informed agent absorbs essentially the whole wealth pool in 4/5 market seeds.
Result 2 (structural negative): the residual-scaling test returned "domain not found." In all 72 population runs, goal dispersion collapsed (V -> 0; maximum 4.85 against a frozen floor of 5.31), the population's response to the two levers was a step function across the dominance boundary rather than a smooth response, and cells near the boundary were bistable with seed-selected outcomes. No tested LLM population at any capability level realizes the noise-maintained-dispersion regime the smooth mean-field model assumes. We release the full protocol, pre-registration chain, call cache, and analysis code.
| Comments: | 15 pages. Preprint. Zenodo: this https URL. Companion synthesis: arXiv:2606.12502 |
| Subjects: | Artificial Intelligence (cs.AI); Multiagent Systems (cs.MA) |
| Cite as: | arXiv:2607.06001 [cs.AI] |
| (or arXiv:2607.06001v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2607.06001 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Cheng Qian [view email]
[v1]
Tue, 7 Jul 2026 08:39:24 UTC (35 KB)
— Originally published at arxiv.org
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