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

Jul 16, 2026

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A pre-registered, two-part experiment tests quantitative laws in coupled multi-agent systems of small economies built from Claude Opus 4.8. The study freezes predictions, acceptance bands, and decision rules in a public git chain, recomputes all reported numbers mechanically from cached outputs, and makes the protocol re-runnable offline. Result 1 confirms an information–wealth “gap law,” coalition submodularity under conditional independence, XOR-driven supermodularity, and an entropy-capped joint growth bound. Result 2 reports a structural failure: residual-scaling returns “domain not found,” with stepwise, seed-sensitive attractor-like behavior rather than smooth mean-field dispersion.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

Abstract

Introduction

Two core questions

Result 1: Coupled capacity region holds

Result 2: Structural negative (residual-scaling test fails)

arXiv :2607 .0600 1v 1 [ cs .AI ] 7 Jul 2026 Information Limits and Attractor Dynamics in Economies of Frontier LLM Agents: A Pre-Registered Test Cheng Qian Independent Researcher Abstract 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 ˆGa − ˆGb = ˆIa − ˆIb 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 ≥ ln 2/2 nats, with agents reasoning out the joint bit; the joint growth ceiling ˆGS ≤ H (X) binds exactly; and the best-informed agent absorbs essentially the whole wealth pool in 4/5 market seeds. This is a quantitative, falsifiable law connecting what an agent measurably knows to what it measurably earns, verified on a frontier model. 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 γ ≷ 12g rather than a smooth response, and cells near the boundary were bistable with seed-selected outcomes. Together with two prior small-model arms (gradient saturation; non-response), no tested LLM population at any capability level realizes the noise-maintained-dispersion regime that smooth mean-field models assume. Near-rational LLM populations behaved as discrete attractor systems—locally near-deterministic, globally seed-sensitive—which suggests that population-level interventions on such systems switch attractors or do nothing, rather than acting marginally. We release the full protocol, pre-registration chain, call cache, and analysis code. 1 Introduction Language-model agents increasingly interact with one another—in simulated societies (Park et al., 2023), in economic simulations (Horton, 2023; Li et al., 2024), and in emerging deployments where multiple model instances trade, bid, negotiate, or compete for resources. Two basic questions about such populations remain largely untested at the frontier-capability level: 1. Does an information-theoretic law govern what LLM agents earn? Classical results connect an agent’s information about an uncertain world to the growth rate of its wealth under repeated betting (Kelly, 1956; Breiman, 1961; Barron & Cover, 1988; Cover & Thomas, 2006) . When agents are coupled through a shared payout mechanism — when one agent’s gain is another’s loss —theory predicts sharp additional structure: relative growth rates should equal relative information, coalition value should exhibit diminishing returns exactly where perception channels are conditionally independent, joint growth should be capped by the world’s entropy, and wealth dynamics should select for the best-informed agent (Blume & Easley, 1992; Sandroni, 2000) . None of this had been measured on real frontier LLM agents. 2. Do LLM populations respond smoothly to incentive and control levers? Mean-field models of populations under selection pressure—of the kind used to reason about steering, regulating, or aligning many-agent systems—typically assume a linear-response regime in

FAQs

What was the main goal of the pre-registered experiment on frontier LLM agents?

To test two quantitative predictions about coupled multi-agent economies: an information-theoretic capacity region for wealth growth and a mean-field residual-scaling law for population misalignment under incentive/control levers.

How were the predictions and reported numbers controlled to ensure determinism?

Predictions, acceptance bands, and decision rules were frozen in a public git chain before runs, and every reported number was recomputed mechanically from cached model outputs, making the experiment re-runnable offline from the cache.

What does the second result say about residual scaling and population dispersion?

The residual-scaling test returned “domain not found,” with goal dispersion collapsing across 72 population runs and responses showing step-function behavior across a dominance boundary, indicating seed-sensitive attractor-like dynamics rather than smooth mean-field scaling.

Jul 16, 2026

Upload by Miles