Supplement Sweeps (B1–B5)¶
Experiments B1–B5 were introduced during paper revision to respond to reviewer critiques on three aspects: parametrisation-dependence of the discontinuous threshold (B1), generality of the reactive < conservative effect (B2), the claim that no regeneration level offsets a single aggressor (B3), conflation of strategic depletion with pure Seneca dynamics (B4), and absence of formal statistical backing (B5).
B1 — Aggressor Intensity: Cliff-Edge Localisation¶
| Attribute | Detail |
|---|---|
| Motivation | Is the "discontinuous step" an artefact of extreme parametrisation (\(i = 0.5\))? |
| Coarse sweep | \(i \in [0.05, 1.00]\), step 0.05; 1 aggressive + 5 conservative; \(r = 0.12\), \(K = 150\) |
| Fine sweep | \(i \in [0.04, 0.11]\), step 0.01; 5–30 runs/cell |
| Result | Cliff edge at \(i \approx 0.05\)–\(0.06\): gate = 100% at \(i = 0.05\), gate = 0% from \(i = 0.06\). Bootstrap 95% CI [0.04, 0.05] (10,000 iterations). Canonical heuristic (\(i = 0.5\)) sits 7–10× above threshold. |
| Figure | aggressive_intensity_sweep__light_paper.png, aggressive_intensity_sweep_fine__light_paper.png |
| Definition | experiments/definitions/aggressive_intensity_sweep.json, aggressive_intensity_sweep_fine.json |
Key Finding — B1
The step-collapse threshold is a structural property of agent-type composition, not a consequence of extreme parametrisation. The canonical aggressor (\(i = 0.5\)) is representative of any strategy that requests a meaningful fraction of available stock; the safe zone (\(i \lesssim 0.05\)) corresponds to extraction so minimal it would not be recognised as aggressive in practice.
B2 — Adaptive Reduction Factor: Generalising the Effect¶
| Attribute | Detail |
|---|---|
| Motivation | Does the reactive < conservative effect hold across different strengths of the adaptive response? |
| Sweep | \(f \in [0, 1.5]\); 1 aggressive (default) + 3 adaptive agents; \(r \in \{0.10, 0.14, 0.20\}\); 20 runs/cell |
| Result | Welfare declines monotonically with \(f\) at all regen rates. Gini rises monotonically. The paradox is graded, not threshold-based: every unit of adaptive reaction incurs proportional welfare cost. |
| Regen Rate | Welfare Slope per unit \(f\) | 95% Bootstrap CI |
|---|---|---|
| \(r = 0.10\) | −14.62 | [−16.39, −13.79] |
| \(r = 0.14\) | −16.17 | [−19.16, −14.26] |
| \(r = 0.20\) | −20.61 | [−22.91, −19.67] |
| Figure | adaptive_reduction_sweep__light_paper.png |
| Definition | experiments/definitions/adaptive_reduction_sweep.json |
Key Finding — B2
The reactive < conservative effect is not a heuristic artefact: it holds continuously across the entire range of adaptive reactivity, with magnitude proportional to \(f\) and steeper at higher regen rates. Partial adaptation is worse than no adaptation.
B3 — Extended Regen Rate: Identifying the Rescue Boundary¶
| Attribute | Detail |
|---|---|
| Motivation | P2 claims "no level of regeneration offsets a single aggressor" within \(r \in [0.04, 0.32]\). Does a rescue point exist at all? |
| Coarse sweep | \(r \in [0.30, 1.50]\), step 0.20; 1 aggressive + 2 conservative + 1 adaptive; \(K = 150\) |
| Fine sweep | \(r \in [0.80, 1.05]\), step 0.025; 5–20 runs/cell |
| Result | Rescue point at \(r \approx 0.95\) (coarse: between \(r = 0.80\) (0%) and \(r = 1.00\) (100%); fine: transition at \(r = 0.925\) → \(r = 0.950\)). Bootstrap 95% CI [0.95, 1.025]. This is nearly an order of magnitude above realistic CPR regeneration rates (\(r \leq 0.32\); 0.95/0.12 ≈ 8× the default \(r\)). |
| Figure | regen_rate_extended__light_paper.png, regen_rate_extended_fine__light_paper.png |
| Definition | experiments/definitions/regen_rate_extended.json, regen_rate_extended_fine.json |
Key Finding — B3
The rescue boundary at \(r \approx 0.95\) corresponds to regeneration matching the scale of combined per-turn extraction. Well-managed fisheries operate at \(r \approx 0.1\)–\(0.3\); tropical forests at \(r < 0.05\). The rescue regime is physically unreachable — making exclusion mechanisms the only viable policy lever.
B4 — Pure Seneca Shock: Isolating Resource Dynamics¶
| Attribute | Detail |
|---|---|
| Motivation | P10's muted Seneca asymmetry could reflect strategic pre-depletion (the aggressor). B4 isolates the pure resource component. |
| Sweep | 4 conservative agents (zero aggressors); shock at turn 20; \(f \in \{0.10, 0.25, 0.50, 0.75, 1.00, 1.50, 2.00\}\); 20 runs/cell |
| Result | Without strategic pre-depletion, negative shocks must be severe (\(f < 0.25\)) to trigger collapse. Moderate shocks (\(f = 0.50\), \(f = 0.75\)) reduce welfare modestly; matched positive shocks provide comparable or larger gains. The Seneca asymmetry is nearly symmetric for moderate magnitudes; it emerges asymmetrically only at extremes. |
| Paired Shocks | Asymmetry Index | Interpretation |
|---|---|---|
| \(f = 0.50\) vs \(f = 1.50\) | +2.0 | Nearly symmetric |
| \(f = 0.25\) vs \(f = 1.50\) | −0.7 | Nearly symmetric |
| \(f = 0.10\) vs \(f = 2.00\) | +18.2 | Positive shocks help more at extremes |
| Figure | pure_seneca_shock__light_paper.png |
| Definition | experiments/definitions/pure_seneca_shock.json |
Key Finding — B4
The bounded Seneca asymmetry in P10 is primarily a strategic artefact: without a co-present aggressor, the logistic commons exhibits near-symmetric shock response. The aggressor pre-loads the system near the collapse cliff, amplifying the apparent Seneca asymmetry by making negative shocks compounding.
B5 — Statistical Inference: Cross-Sweep Analysis¶
| Attribute | Detail |
|---|---|
| Motivation | Formal statistical testing for all platform findings |
| Methods | Logistic regression of gate pass rate on canonical covariates (167 cells pooled from all 17 sweeps); bootstrap CIs (10,000 iterations resampling cells); permutation tests for stochastic sweeps |
| Result | Two covariates have bootstrap CIs robustly excluding zero: regen rate (+39.5 [23.2, 76.4]) and aggressive count (−32.2 [−62.1, −19.2]). Aggressor intensity is borderline (CI [−127.8, +0.9]). Pool size coefficient (+1.8) reflects composition confound, not structural benefit. Scheduler differences: formally not distinguishable (\(p > 0.05\) by permutation). |
| Predictor | Coefficient | 95% Bootstrap CI | Robust? |
|---|---|---|---|
| aggressor intensity | −66.0 | [−127.8, +0.9] | Borderline |
| regen rate | +39.5 | [+23.2, +76.4] | ✓ |
| aggressive count | −32.2 | [−62.1, −19.2] | ✓ |
| adaptive reductionFactor | −5.7 | [−34.8, +3.1] | ✗ |
| pool size (\(N\)) | +1.8 | [+0.9, +3.8] | ✓ |
Key Finding — B5
Formal inference confirms: aggressive count and regen rate are the only covariates with CIs robustly excluding zero. The cliff edge (\(i \approx 0.05\)–\(0.06\)) and rescue boundary (\(r \approx 0.95\)) are quantified with explicit CIs. Scheduler differences in welfare and game length are statistically indistinguishable (\(p > 0.05\)).
Files¶
All 17 sweep definitions are in experiments/definitions/. Run with: