# Information Limits and Attractor Dynamics in Economies of Frontier LLM Agents: A Pre-Registered Test

arXiv: https://arxiv.org/abs/2607.06001 · HTML: https://mlsanity.com/paper/2607.06001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 5 of 5)

- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Multi-Agent Risks from Advanced AI](https://mlsanity.com/paper/2502.14143/) (2025)
- [EconAgent: Large Language Model-Empowered Agents for Simulating Macroeconomic Activities](https://mlsanity.com/paper/2310.10436/) (2023)
- [AI Research Considerations for Human Existential Safety (ARCHES)](https://mlsanity.com/paper/2006.04948/) (2020)
- [A Mathematical Theory of Value: a synthesis on goal-directed agency under resource constraints](https://mlsanity.com/paper/2606.12502/) (2026)

## Abstract (arXiv)

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 Ga - Gb = Ia - Ib 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 GS <= 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.