A Factorial Agent-Based Study
Fifth paper in the complexity-econ series. Tests whether the universality of AI adoption phase transitions (established in Paper 04) survives when both the sectoral elasticity of substitution (σ) and the inter-firm network are made endogenous.
- The reentrant (inverted-U) adoption shape survives in all four factorial cells
- Endogenous σ preserves BDP_c = 500 PLN up to moderate learning rates (λ ≤ 0.02)
- Dynamic network rewiring shifts BDP_c to 750 PLN for intermediate rates (ρ ∈ [0.02, 0.10])
- The combined effect is superadditive (+6.5 pp peak adoption vs. baseline)
- Endogenous σ does not produce self-organized criticality (SOC)
2×2 factorial: (fixed/endogenous σ) × (static/dynamic network), plus two marginal sensitivity sweeps.
| Campaign | Simulations | Description |
|---|---|---|
| C1 Factorial | 2,520 | 4 cells × 21 BDP × 30 seeds |
| C2 Lambda | 3,780 | 6 λ values × 21 BDP × 30 seeds |
| C3 Rho | 3,780 | 6 ρ values × 21 BDP × 30 seeds |
| Total | 10,080 |
Fig 1. Adoption vs BDP across all four factorial cells. The reentrant (inverted-U) shape survives endogenization — static cells peak at BDP_c = 500, dynamic network cells shift to BDP_c = 750.
Fig 2. Adoption difference relative to the static/static baseline. The full endogenous cell (red) peaks at +6.7 pp — effects are superadditive near the critical region.
Fig 3. Terminal σ at month 120 for each sector under learning-by-doing (λ = 0.02). BPO/SSC nearly doubles its elasticity; low-digital sectors (Public, Agriculture) barely move — a Matthew effect in technology diffusion.
Fig 4. Heatmap of σ fold change across all BDP levels and sectors. The strongest growth occurs in the critical region (BDP 250–750), not at the highest subsidies.
Fig 5. Mean degree at month 120 across factorial cells. Static cells hold at ⟨k⟩ = 6; dynamic rewiring causes modest decline from death-birth turnover.
Fig 6. Mean degree vs BDP for different rewiring rates ρ. Higher ρ increases degree variation but the mean stays close to the initial k = 6.
Fig 7. Adoption curves for each learning rate λ. Higher λ raises peak adoption monotonically while preserving the reentrant shape.
Fig 8. Critical BDP vs learning rate. BDP_c is rock-stable at 500 for λ ≤ 0.02, then jumps discretely to 750 at λ ≥ 0.05 — a threshold effect.
Fig 9. Adoption curves for each rewiring rate ρ. Moderate rewiring boosts adoption near criticality; excessive rewiring shows diminishing returns.
Fig 10. Critical BDP vs rewiring rate — strikingly non-monotonic. Preferential attachment shifts BDP_c to 750 at intermediate ρ, but high ρ destroys network structure faster than it forms, reverting to BDP_c = 500.
Fig 11. Susceptibility proxy (variance peaks) across all four cells. Peaks cluster in the BDP 250–750 band — the critical region is only mildly perturbed by endogenization.
Fig 12. SOC diagnostic: σ does not converge to a critical attractor. Instead, a positive feedback loop (adoption → σ growth → more adoption) amplifies the transition without self-tuning.
analysis/python/ — 7 analysis scripts generating 12 figures
figures/ — Generated PNG figures (200 DPI)
latex/ — Paper source (XeLaTeX + biblatex)
simulations/
scripts/ — Campaign runner scripts
results/ — Terminal CSV files (European format)
- Engine: complexity-econ/core (Scala 3.5.2, sbt)
- Analysis: Python 3 (matplotlib, numpy, pandas, seaborn)
- Paper: XeLaTeX + biblatex
# Run all simulation campaigns (~3h on M-series Mac)
cd simulations/scripts && bash run_all.sh
# Generate all figures
cd analysis/python && for f in factorial_bifurcation sigma_trajectories network_evolution lambda_sensitivity rho_sensitivity universality_test; do python3 ${f}.py; done
# Compile paper
cd latex && xelatex paper_en.tex && bibtex paper_en && xelatex paper_en.tex && xelatex paper_en.tex| # | Paper | DOI |
|---|---|---|
| 01 | The Acceleration Paradox | 10.5281/zenodo.18727928 |
| 02 | Monetary Regime & Automation | 10.5281/zenodo.18740933 |
| 03 | Empirical σ Estimation | 10.5281/zenodo.18743780 |
| 04 | Phase Diagram & Universality | 10.5281/zenodo.18751083 |
| 05 | Endogenous Technology & Networks | 10.5281/zenodo.18758365 |
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