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
A pre-registered experiment on Claude Opus 4.8 investigates wealth growth and population misalignment in economies, revealing that relative growth aligns with claimed information but fails to demonstrate expected noise-maintained dispersion. 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 LLM population achieved the noise-maintained dispersion assumed by the smooth mean-field model.
- Experiment protocol, pre-registration chain, and analysis code are publicly available.
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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