Llm Agent Economies Information Limits

---
name: llm-agent-economies-information-limits
description: "Pre-registered experiment on small economies of frontier LLM agents (Claude Opus 4.8), testing information-theoretic capacity regions for wealth growth under market coupling and mean-field residual attractor dynamics. Activation: LLM agent economies, information-theoretic capacity, mean-field dynamics, attractor dynamics, market coupling, multi-agent simulation, wealth growth."
metadata:
  arxiv_id: "2607.06001"
  published: "2026-07-07"
  authors: "Cheng Qian"
  tags: [llm-agent-economies, information-theory, mean-field-dynamics, attractor-dynamics, market-coupling, multi-agent-simulation, wealth-growth]
---

# Information Limits and Attractor Dynamics in Economies of Frontier LLM Agents

## Overview

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-attractor dynamics model.

## Key Innovations

### Information-Theoretic Capacity Region
- Predicts the maximum wealth growth rate achievable by LLM agents under market coupling
- Frames multi-agent economic interaction as an information-theoretic channel
- Capacity region defines the boundary of achievable economic outcomes

### Mean-Field Residual-Attractor Dynamics
- Models the dynamics of LLM agent economies using mean-field theory
- Residual attractor: the system converges to predictable equilibrium despite agent heterogeneity
- Connects microscopic agent behavior to macroscopic economic patterns

### Pre-Registered Experiment
- Predictions registered before data collection (reduces p-hacking risk)
- Uses frontier LLM (Claude Opus 4.8) as economic agents
- Small-economy setting enables controlled experimentation

## Methodology

1. **Agent Setup**: Frontier LLM agents act as economic actors in a market simulation
2. **Market Coupling**: Agents interact through market mechanisms (trade, pricing, etc.)
3. **Wealth Tracking**: Measure wealth distribution and growth across agents
4. **Information-Theoretic Analysis**: Test whether growth rates respect predicted capacity bounds
5. **Dynamics Analysis**: Fit mean-field residual-attractor model to observed dynamics
6. **Pre-Registration**: Hypotheses and analysis plan registered before experiment

## Implications

- LLM agents as a testbed for economic theory: controlled, reproducible experiments
- Information-theoretic framework for understanding multi-agent economic systems
- Mean-field theory as a bridge between individual agent behavior and system-level dynamics
- Pre-registered methodology sets a standard for experimental rigor in agentic AI research
- Insights into how frontier LLMs behave in economic settings (rationality, strategy, cooperation)

## Pitfalls

- Small economy size may not generalize to larger multi-agent settings
- LLM agent behavior may not reflect human economic behavior
- Pre-registration is valuable but doesn't eliminate all experimental biases
- Mean-field approximations may break down with heterogeneous agents
- Single LLM (Claude Opus 4.8) limits generalizability across model families
- Economic simulation design (market rules, initial conditions) strongly affects outcomes

## Activation Keywords

LLM agent economies, information-theoretic capacity, mean-field dynamics, attractor dynamics, market coupling, multi-agent simulation, wealth growth, economic simulation, pre-registered experiment

## Paper Reference

arXiv:2607.06001 - "Information Limits and Attractor Dynamics in Economies of Frontier LLM Agents" (Jul 2026)