3 Experiments

Four mini-pilots verify the governance MVP. C1 (3 players, $N = 5$ seeds) checks that the sanction mechanism fires deterministically against detected violations. D1 (6 players, $N = 5$ seeds) decomposes the effect of agent architecture and cheap-talk communication at the canonical BDPD$^0$ cliff configuration via a $2 \times 2$ factorial design. D2 (5 players, $N = 5$ seeds) compares graduated vs flat sanctioning under identical pact and LLM conditions. D3 (5 players, $N = 5$ seeds) sweeps the shape of the graduated ladder to isolate which feature of the $[1, 3, 10]$ baseline carries the D2 effect.

The four pilots span two substrate calibrations. D1 reuses the canonical BDPD$^0$ cliff ($K = 150$, $r = 0.12$, 6 players) so the architecture-vs-talk decomposition is directly comparable with the baseline cliff finding. C1, D2, and D3 use a tighter substrate ($K = 100$, $r = 0.10$, 3–5 players) because the sanction perturbations extend run length significantly and a smaller commons keeps each pilot runnable in $\le 30$ turns on a single seed while preserving the qualitative cliff dynamics. Table 3.1 summarises the four configurations side-by-side.

Table 3.1: Pilot overview. All pilots run N = 5 seeds per cell with deepseek-v4-flash (thinking off) on LLM cells. Player composition is given as conservative + aggressive archetypes. Tool surface refers to the cheap-talk and pact primitives exposed to LLM agents; “none” means an empty tool list (built-in agents, or the --no-talk LLM cell).

Pilot	Players (c+a)	K	r	Tool surface	Sanction	Question tested
C1	3 (2+1)	100	0.10	full	flat 3	mechanism: do sanctions fire 1:1 on detected violations?
D1	6 (5+1)	150	0.12	A: none, B: full, C: none	off	architecture vs cheap-talk at the cliff
D2	5 (4+1)	100	0.10	full	A: ladder [1,3,10], B: flat 3	graduated vs flat sanctioning
D3	5 (4+1)	100	0.10	full	[1,2,4], [1,5,25], [5,5,5]	escalation shape vs raw amount

All LLM-driven runs use deepseek-v4-flash with thinking disabled, temperature 0.4, and the platform default prompt. They live on a single host with one Python subprocess per LLM-driven player. C1 sweeps the legacy seed set $\{17, 42, 123, 456, 789\}$ from its pre-standardisation mechanism check; D1, D2, and D3 sweep the project anchor set $\{17, 23, 29, 31, 37\}$ (5 primes including the BDPD$^0$ anchor seed 17) so the three D-pilots are seed-aligned for the preservation table in Chapter 4. Source scripts:

scripts/pilot_{c1,d1_n5,d1_cell_c,
d2_llm_n5,d2_ladder_sweep}.mjs
scripts/plot_{d1_n5,d2_llm_n5,
d2_ladder_sweep}.py

Raw artefacts are regenerated under data/pilot/{c1,d1_n5,d1_cell_c,d2_llm_n5,d2_ladder_sweep}/ when the scripts are run with DEEPSEEK_API_KEY set; this directory is intentionally git-ignored (runtime artefacts, not versioned).

3.1 C1 — Sanction mechanism in silico

An $N = 5$ mini-pilot that the sanction perturbation fires deterministically against detected pact violations.

3.1.1 Setup

Parameter	Value
Players	3 (`alice`, `bob` conservative; `carol` aggressive)
Initial private capital	$30$ per player (so the $\text{amount} = 3$ sanction is $10\%$ of starting wealth)
Commons	$K = 100$, initial $= 50$, $r = 0.10$, threshold $= 10$
Pre-injected pact	`harvest_cap`, `maxHarvest = 0.5`, all three parties accept
Sustainable share	$\approx 0.83$ per player at $T_1$ (cap is below it)
Sanction	`pact_violation(harvest_cap)` $\to$ `amount = 3`
Max turns	7
Seeds	$\{17, 42, 123, 456, 789\}$

The cap is set below the sustainable share, so honouring it is a strict cost.

3.1.2 Result

The mechanism fires 1:1 in every seed: a per-seed total of $3 \pm 1.8$¹ detected violations across the three players (carol $2.8 \pm 1.7$, bob $0.2 \pm 0.4$, alice $0$; range $1$–$6$) produced an equal count of sanction events.

Player	Harvested ($\mu \pm \sigma$)	Violations	Sanctions	Final wealth ($\mu \pm \sigma$)
`alice` (conservative)	$3.5 \pm 0.0$	$0.0 \pm 0.0$	$0.0 \pm 0.0$	$\mathbf{33.50 \pm 0.00}$
`bob` (conservative)	$3.8 \pm 0.6$	$0.2 \pm 0.4$	$0.2 \pm 0.4$	$33.16 \pm 0.59$
`carol` (aggressive)	$7.9 \pm 2.0$	$2.8 \pm 1.7$	$2.8 \pm 1.7$	$29.46 \pm 3.54$

Two qualitative observations are worth recording. First, carol violates in every seed (range $1$–$6$ violations), typically opening with a turn or two at the cap before defecting. The cumulative monetary loss therefore grows with each repeated violation under a constant-amount sanction, producing a graduation-like effect on the violator’s wealth path without any explicit ladder; this is the implementation-incidental cousin of the graduated-sanction principle (Ostrom #5), not a deliberate ladder. Second, the conservative players are largely but not perfectly insulated from a defector: alice held the cap in every seed ($0$ violations), while bob slipped on a single seed ($1$ violation vs $0$ in the other four). We avoid claiming a strong analogy to BDPD$^0$’s reactive < conservative finding here: the mechanism is different (pact-violation rather than harvest-reaction) and the LLM cognitive substrate adds its own sources of seed-level variance. The contagion-like pattern is seed-variable rather than universal, which is itself informative: the conservative archetype’s behavioural prior is robust on average but not deterministic.

3.1.3 Diagnosis

The sanction layer is operational: each detected violation produces exactly one sanction event (the 1:1 firing reported above), so the detection-to-sanction chain never leaks. The sanction_rate metric (sanctioned players over nPlayers, i.e. $\approx k/N$ for $k$ players sanctioned on a turn) is non-zero on every violation turn and moves dynamically through the run. Mechanism verified.

3.2 D1 — Architecture vs communication at the cliff

The original D1 design compared built-in agents (no talk) against LLM agents (with talk), varying two factors simultaneously — agent architecture and communication channel — confounding the two effects. Cell C — LLM agents with the cheap-talk tool surface disabled (--no-talk) — was added to decompose them. The three cells form an incomplete $2 \times 2$ factorial:

	No talk	Talk
Built-in	Cell A	(empty — built-in agents cannot use language)
LLM	Cell C	Cell B

The design is a structurally incomplete $2 \times 2$: the built-in + talk cell is not implemented in this study. A heuristic agent could in principle be equipped with a fixed broadcast template (e.g. “I plan to harvest $X$”) and so participate in the talk channel mechanically, but the resulting messages would not be adaptive signals — they would simply replay the agent’s deterministic strategy — and the comparison would conflate mechanical broadcasting with adaptive cheap talk. We treat that cell as out of scope rather than impossible. This makes the present design a decomposition layout, not a classical ANOVA factorial. It isolates the main effect of architecture (A vs C) and the marginal effect of talk given LLM agents (C vs B), but cannot estimate the architecture $\times$ talk interaction.

3.2.1 Setup

All three cells run at the canonical BDPD$^0$ cliff, replicated across $N = 5$ seeds:

Parameter	Cell A	Cell B	Cell C
Players	6 built-in	6 LLM	6 LLM
Archetypes	5 cons. + 1 aggr.	5 cons. + 1 aggr.	5 cons. + 1 aggr.
Engine	`logistic`	`logistic`	`logistic`
$K$	150	150	150
$r$	0.12	0.12	0.12
Threshold	10	10	10
Max turns	30	30	30
Tool surface	none	full cheap-talk + pact	none (`--no-talk`)
Sanctioning	OFF	OFF	OFF
Seeds	$\{17, 23, 29, 31, 37\}$	same	same

Cell A is fully deterministic: the five seeds produced identical trajectories (collapse to a residual $4.39$-unit stock at $T = 24$). Cell C agents use the same LLM, prompt, and memory as Cell B but receive no communication tools and no announced field in the response schema — they can observe their peers’ harvests but cannot signal intentions.

3.2.2 Result

Figure 3.1: D1 three-cell decomposition ($N = 5$ LLM seeds). *Left:* commons stock trajectory, mean $\pm$ sd across seeds, all three cells. Cell A (green, solid) is the built-in baseline: deterministic, landing on the same near-collapse residual at $T = 24$ on every seed ($0/5$ reach $T = 30$). Cell C (blue, dash-dot) is LLM agents *without* talk: it preserves the commons in $4/5$ seeds and carries the headline architecture effect (A $\to$ C). Cell B (red, dashed) is LLM agents *with* talk: a $\sigma \approx 26$ band with only $2/5$ seeds reaching $T = 30$, i.e. talk adds no preservation over Cell C. *Right:* final wealth by archetype, mean $\pm$ sd across seeds. The aggressor’s wealth is highest in Cell C ($\sim 177$) and drops in Cell B ($\sim 119$) while conservators gain — the signature of talk’s redistributive, not preservative, role.

Figure 3.1 shows the headline trajectories. Metrics across the three cells are collected in Table 3.2:

Table 3.2: D1 decomposition metrics at $N = 5$ seeds. Cell A is deterministic, so its silent_defection value ($0.72$) is the built-in aggressor’s fixed over-harvest fraction — well-defined, but reported for completeness rather than as a channel-based rate comparable to Cell B. Cell C silent_defection is non-comparable (n/c): without an announcement channel, every over-harvester is mechanically “silent”. Cell B’s low $\sigma$ on silent_defection ($0.07$) may reflect the binary nature of the announcement channel rather than a causal relationship with preservation.

Metric	Cell A (builtin)	Cell B (LLM + talk)	Cell C (LLM, no talk)
Turns survived	$24 \pm 0$	$24 \pm 5$	$29.8 \pm 0.4$
Reached $T = 30$	0 / 5	2 / 5	4 / 5
Final commons stock	$4.4 \pm 0$	$23 \pm 26$	$28 \pm 26$
`cooperation_index` $\mu$	$0.28$	$0.43 \pm 0.10$	$0.50 \pm 0.03$
`announce_frequency` $\mu$	$0$	$0.50 \pm 0.06$	$0$ (no channel)
`silent_defection` $\mu$	$0.72$	$0.38 \pm 0.07$	n/c (no channel)
`lie_score` $\mu$	n/a	$0.001$ (max $0.003$)	n/a
Aggressor final wealth	$139$	$119 \pm 19$	$177 \pm 20$
Mean conservator wealth	$53.0$	$54.4 \pm 3.1$	$46.6 \pm 1.7$

The factorial decomposition yields three findings.

Architecture is the dominant effect. The transition from built-in to LLM agents without any communication (A $\to$ C) raises cooperation_index from $0.28$ to $0.50$ and extends the game from $24$ to $\sim 30$ turns. The cooperation lift is entirely architectural: LLM agents, given only harvest observations, already extract more conservatively than the heuristic baseline. This is consistent with independent evidence that LLMs exhibit intrinsic prosocial tendencies in canonical strategic games, cooperating well above human baselines even without communication (e.g. $\sim 65 \%$ vs $\sim 37 \%$ in the prisoner’s dilemma (Brookins and DeBacker 2024)).

Cheap-talk does not improve commons preservation. Comparing Cell C (LLM, no talk) against Cell B (LLM, with talk), the final stock is $28 \pm 26$ vs $23 \pm 26$ — a difference of $\sim 5$ units against a pooled $\sigma$ of $\sim 26$ (Cohen’s $d = 0.17$). The effect, if real, is negligible; a power analysis yields $n \approx 540$ per cell to detect it at $80\%$ power. cooperation_index is marginally lower in Cell B ($0.43$) than in Cell C ($0.50$), confirming that adding the talk channel does not make agents cooperate more. This null contrasts with classic collective-risk experiments where communication helps groups coordinate toward a shared threshold (Milinski et al. 2008): on the BDPD cliff the threshold is not collective but individual — a single aggressor suffices — and communication cannot deter a player whose privately optimal strategy is over-extraction regardless of what others say.

Talk redistributes wealth, not commons. The aggressor’s final wealth drops from $177$ (Cell C) to $119$ (Cell B) — a $\sim 33\%$ reduction. Conservators’ mean wealth rises from $46.6$ to $54.4$ ($\sim +17\%$). The pattern is consistent with a coordination mechanism: conservators use the broadcast channel to signal against the defector, reducing the defector’s relative advantage. Talk is an instrument of equity rather than preservation.

Lying does not emerge. Cell B’s lie_score is essentially zero (mean $0.001$, max $0.003$ across seeds; $3$ of $5$ seeds exactly $0$): when LLM agents announce, they honour the announcement essentially perfectly.

3.2.3 Diagnosis

At the canonical cliff configuration, the original two-cell design confounded two effects. Cell C resolves the confound: the cooperation lift attributed to cheap-talk in the original analysis is in fact an architectural effect of switching from heuristic to LLM agents. Cheap-talk alone does not improve commons preservation at this scale, but it does redistribute wealth from the defector to the conservators. The natural next question — does adding an enforcement layer produce a clean preservation signal? — is exactly what D2 tests.

3.3 D2 — Graduated sanctions in silico (Ostrom #5)

Does a graduated sanction ladder preserve the commons more reliably than a flat sanction of equivalent expected cost?

3.3.1 Setup

Two cells side-by-side under LLM cognition, identical except for the shape of the sanction triggered on a pact_violation:

Parameter	Cell A (graduated)	Cell B (constant)
Players	5 LLM (4 conservative + 1 aggressive)	same
Engine	`logistic`, $K=100$, $r=0.10$	same
Commons initial	80	same
Threshold	10	same
Max turns	30	same
Pre-injected pact	`harvest_cap`, $\text{maxHarvest}=2.0$, 5 parties accept	same
Sanction trigger	`pact_violation(harvest_cap)`	same
Sanction payload	`ladder = [1, 3, 10]` (per ordinal)	`amount = 3` (flat)
Seeds	$\{17, 23, 29, 31, 37\}$	same
Model	`deepseek-v4-flash` no-think	same

The cap is above the conservative archetype’s natural harvest at ratio $> 0.6$ ($\approx 1.5$) and below the aggressive archetype’s ($\approx 2.5$). Conservatives can honour the cap costlessly; aggressors face a real cost. The two cells differ only in whether the sanction amount scales with violation ordinal.

Cell A draws from the sanction_graduated perturbation type described in this paper. The handler counts prior $(player, \text{termType})$ violations in the pact registry and selects ladder[min(\text{ordinal}-1, \text{len}-1)] — last value sticks.

3.3.2 Result

Figure 3.2: D2 headline (N=5 LLM seeds). Left: commons stock per turn, mean $\pm$ sd across seeds (faint lines: individual seeds). Cell A (graduated, green solid) preserves the commons in all five seeds to $T = 30$. Cell B (constant, red dashed) preserves it in three, with the other two collapsing at $T = 12$ and $T = 26$. Right: defector (the designated aggressive over-extractor, termed *mule* in BDPD$^0$) cumulative sanction loss; the two distributions overlap fully, i.e. *individual-level* deterrence is not robust at this $n$.

Figure 3.2 shows the headline trajectories. Statistics across the five seeds:

Table 3.3: D2 headline metrics, $n = 5$ seeds.

Metric	Cell A grad ($\mu \pm \sigma$)	Cell B const ($\mu \pm \sigma$)
Turns survived	$30.0 \pm 0.0$ [30, 30]	$25.6 \pm 7.8$ [12, 30]
Commons preserved at $T=30$	5 / 5	3 / 5
Total violations	$6.2 \pm 6.2$ [0, 14]	$11.8 \pm 12.7$ [0, 30]
Final commons stock	$26 \pm 8$	$24 \pm 14$
Defector final wealth	$55 \pm 43$	$57 \pm 29$
Conservator mean wealth	$43 \pm 4$	$43 \pm 3$

One discriminating outcome survives: the binary survival rate (reached $T = 30$ without collapse). Five of five Cell A seeds preserve the commons; three of five Cell B seeds do. The two collapses in Cell B (seeds $\{29, 37\}$ in the sample drawn) are at $T = 12$ and $T = 26$ — the constant-3 schedule fails to deter sustained over-extraction.

Most other claims do not survive at this $n$. Defector final wealth spans an observed range (min–max across the five seeds) of $[7, 90]$ in Cell A and $[21, 90]$ in Cell B — fully overlapping. Total violations are nominally halved by the ladder, but the cell-A standard deviation equals its mean. One seed (31) is inverted: Cell A registers 14 violations while Cell B registers none.

3.3.3 Diagnosis

The graduated schedule’s robust effect at the mini-pilot scale is preservation of the commons; the fine-grained deterrence narrative — the “first –10 shock teaches the group” reading available on any single seed — does not generalise across seeds at $n = 5$. We report the binary survival rate as the load-bearing claim of D2, and reserve the individual-deterrence and social-transmission narratives for the future campaign at $N \geq 20$. The result is consistent with Ostrom’s design-principle #5 (graduated sanctions) interpreted at the population level, and provides the first positive governance signal that the paper places alongside the D1 cheap-talk noisy-positive.

3.4 D3 — Ladder geometry sweep

D2 showed graduated $>$ flat. The follow-up question: is it the escalation shape that matters, or the high terminal amount?

3.4.1 Setup

D3 holds the D2 setup fixed (5 LLM agents, 4 conservative + 1 aggressive, $K = 100$, $r = 0.10$, threshold $= 10$, pre-injected harvest_cap = 2.0 pact, seeds $\{17, 23, 29, 31, 37\}$, 30-turn cap, deepseek-v4-flash no-think) and varies only the ladder payload of the sanction_graduated perturbation:

Cell	Ladder	Reading
A	$[1, 2, 4]$	Soft escalation
B	$[1, 5, 25]$	Hard escalation
C	$[5, 5, 5]$	Flat-5 — control: high amount, no graduation

The D2 baseline $[1, 3, 10]$ ($5/5$) sits between A and B on the escalation curve and serves as the reference. Cell C is the critical control: if a constant high amount preserves the commons, then “amount” is what matters; if it fails, then the escalation shape itself is the load-bearing feature.

3.4.2 Result

Figure 3.3: D3 ladder-geometry sweep ($N = 5$ LLM seeds, 3 ladder shapes overlaid against the D2 baseline $[1, 3, 10]$). Left: commons stock mean $\pm$ sd across seeds, all three cells. Cells A (soft, green) and B (hard, red dashed) both stay well above threshold for most seeds; Cell C (flat-5, grey dotted) trails to threshold by $T = 17$–$28$ on $4/5$ seeds. Right: preservation rate (count of seeds reaching $T = 30$).

Figure 3.3 compares the three geometries. Statistics by ladder shape (with D2 baseline $[1, 3, 10]$ inserted for reference) appear in Table 3.4:

Table 3.4: D3 + D2 ladder geometry comparison, $N = 5$ seeds each. † row reproduced from Table 3.3 for reference. The $4/5$ count for $[1, 2, 4]$ reflects a single non-T=30 seed (seed 17, which closed at $T = 29$ with $S = 11.6$ — still above the threshold $\theta = 10$ but one turn short of the cap, so it is counted as not having reached $T = 30$ under the strict preservation criterion used throughout the paper).

Ladder	Reached $T = 30$	Turns ($\mu \pm \sigma$)	Final stock ($\mu \pm \sigma$)	Mule wealth ($\mu \pm \sigma$)
$[1, 2, 4]$	$4 / 5$	$29.8 \pm 0.4$	$22 \pm 13$	$78 \pm 20$
$[1, 3, 10]$ †	$5 / 5$	$30 \pm 0$	$26 \pm 8$	$55 \pm 43$
$[1, 5, 25]$	$5 / 5$	$30 \pm 0$	$38 \pm 5$	$\mathbf{22 \pm 34}$
$[5, 5, 5]$	$\mathbf{1 / 5}$	$23 \pm 6$	$10 \pm 2$	$65 \pm 19$

The critical control fails. Cell C $[5, 5, 5]$ — a constant amount roughly halfway between the canonical ladder’s extremes ($1$ and $10$) — preserves the commons in only $1/5$ seeds, against $4/5$–$5/5$ for the three graduated ladders. A high amount applied uniformly is not sufficient.

The escalation shape carries the effect. All three graduated ladders preserve the commons in at least $4/5$ seeds, including the soft $[1, 2, 4]$ whose terminal value ($4$) is below the flat-5 control’s amount ($5$). The differentiator is not the magnitude of the sanction but the temporal profile — starting low and rising. This echoes recent experimental evidence from human-subject CPR games, where graduated sanctioning outperforms strict sanctioning in the long run by reducing retaliatory responses and increasing perceived legitimacy (Klingeren and Buskens 2024); the mechanism is formalised in evolutionary models of risky public-goods governance, which show that escalation schedules promote cooperation at lower average severity than flat sanctions and are most effective when implementation costs scale with severity (Couto et al. 2020).

Wealth-preservation trade-off. Among the graduated cells, the defector outcome differs sharply:

$[1, 2, 4]$: defector wealth $\sim 78$ (high) — soft escalation preserves the commons but leaves the violator largely intact; deterrence works through near-zero violations rather than punishment severity.
$[1, 3, 10]$: $55 \pm 43$ — intermediate, with the highest variance because the third tier is hit unpredictably.
$[1, 5, 25]$: $\mathbf{22 \pm 34}$ — hard escalation is punitive: the third tier strips the violator on the seeds where it fires, dropping defector wealth by $\sim 75\%$ vs the soft ladder.

The three graduated cells thus span a Pareto frontier between final commons stock and violator-wealth retention (stock $22 / 26 / 38$ against wealth $\sim 78 / 55 / 22$ for $[1, 2, 4] / [1, 3, 10] / [1, 5, 25]$) rather than a single dominated point; on the binary preservation rate alone the frontier would degenerate, so the continuous stock is the discriminating axis.

3.4.3 Diagnosis

Cell C’s failure rules out “high amount” as the operative mechanism behind D2’s $5/5$. The graduated ladders preserve the commons because they escalate, not because they hit hard. Three secondary observations are worth noting against a future campaign:

Soft graduation $[1, 2, 4]$ trades a marginal preservation drop ($4/5$ instead of $5/5$) for a clean wealth-retention outcome on the violator.
Hard graduation $[1, 5, 25]$ achieves both $5/5$ preservation and strong violator-wealth ablation, but with the highest cross-seed variance on defector wealth ($\sigma = 34$ on a $\mu = 22$).
A campaign-scale ladder sweep (denser shape grid, $N \geq 30$) would resolve whether the preservation– punishment trade-off is monotone in $\Delta(\text{ladder}_3, \text{ladder}_1)$ or admits non-monotonic regimes.

While speculative at this scale, the graduated structure echoes real-world sanction design: progressive penalty schedules (e.g. EU ETS escalating surrender obligations) outperform one-shot mega-fines that firms can internalise as a cost of doing business.

All numeric summaries in this paper retain enough precision to cross-check the per-seed aggregate.json artefacts under data/pilot/. At $N = 5$, the reported standard deviations are diagnostic of cross-seed spread, not statistical confidence bounds: distributions whose $\sigma$ approaches or exceeds $\mu$ — for instance the defector wealth in Section 3.3 and Section 3.4 — reflect fully overlapping seed-level ranges and are reported for transparency, not as estimates of population parameters. Because the governance pilots are LLM-mediated, the absolute per-seed counts here (and in Section 3.3, Section 3.4) are one realization of a non-deterministic process; the 1:1 violation-to-sanction firing is the invariant that holds across realizations, not the exact counts. See Section 4.4 on the non-pinnable cloud checkpoint and why these numbers are directional rather than point estimates. The non-violator wins on wealth across all 5 replicates:↩︎

# Experiments {#sec-experiments} Four mini-pilots verify the governance MVP. C1 (3 players, $N = 5$ seeds) checks that the sanction mechanism fires deterministically against detected violations. D1 (6 players, $N = 5$ seeds) decomposes the effect of agent architecture and cheap-talk communication at the canonical BDPD$^0$ cliff configuration via a $2 \times 2$ factorial design. D2 (5 players, $N = 5$ seeds) compares graduated vs flat sanctioning under identical pact and LLM conditions. D3 (5 players, $N = 5$ seeds) sweeps the *shape* of the graduated ladder to isolate which feature of the $[1, 3, 10]$ baseline carries the D2 effect. The four pilots span two substrate calibrations. D1 reuses the canonical BDPD$^0$ cliff ($K = 150$, $r = 0.12$, 6 players) so the architecture-vs-talk decomposition is directly comparable with the baseline cliff finding. C1, D2, and D3 use a tighter substrate ($K = 100$, $r = 0.10$, 3–5 players) because the sanction perturbations extend run length significantly and a smaller commons keeps each pilot runnable in $\le 30$ turns on a single seed while preserving the qualitative cliff dynamics. @tbl-pilot-overview summarises the four configurations side-by-side. | Pilot | Players (c+a) | K | r | Tool surface | Sanction | Question tested | |-------|:------------:|:---:|:----:|--------------|----------|------------------| | C1 | 3 (2+1) | 100 | 0.10 | full | flat 3 | mechanism: do sanctions fire 1:1 on detected violations? | | D1 | 6 (5+1) | 150 | 0.12 | A: none, B: full, C: none | off | architecture vs cheap-talk at the cliff | | D2 | 5 (4+1) | 100 | 0.10 | full | A: ladder [1,3,10], B: flat 3 | graduated vs flat sanctioning | | D3 | 5 (4+1) | 100 | 0.10 | full | [1,2,4], [1,5,25], [5,5,5] | escalation shape vs raw amount | : Pilot overview. All pilots run N = 5 seeds per cell with `deepseek-v4-flash` (thinking off) on LLM cells. Player composition is given as conservative + aggressive archetypes. *Tool surface* refers to the cheap-talk and pact primitives exposed to LLM agents; "none" means an empty tool list (built-in agents, or the `--no-talk` LLM cell). {#tbl-pilot-overview} All LLM-driven runs use `deepseek-v4-flash` with thinking disabled, temperature 0.4, and the platform default prompt. They live on a single host with one Python subprocess per LLM-driven player. C1 sweeps the legacy seed set $\{17, 42, 123, 456, 789\}$ from its pre-standardisation mechanism check; D1, D2, and D3 sweep the project anchor set $\{17, 23, 29, 31, 37\}$ (5 primes including the BDPD$^0$ anchor seed 17) so the three D-pilots are seed-aligned for the preservation table in @sec-discussion. Source scripts: - `scripts/pilot_{c1,d1_n5,d1_cell_c,`\ `d2_llm_n5,d2_ladder_sweep}.mjs` - `scripts/plot_{d1_n5,d2_llm_n5,`\ `d2_ladder_sweep}.py` Raw artefacts are regenerated under `data/pilot/{c1,d1_n5,d1_cell_c,d2_llm_n5,d2_ladder_sweep}/` when the scripts are run with `DEEPSEEK_API_KEY` set; this directory is intentionally git-ignored (runtime artefacts, not versioned). ## C1 — Sanction mechanism in silico {#sec-c1} An $N = 5$ mini-pilot that the sanction perturbation fires deterministically against detected pact violations. ### Setup | Parameter | Value | |---------------------|-------------------------------------------------------------| | Players | 3 (`alice`, `bob` conservative; `carol` aggressive) | | Initial private capital | $30$ per player (so the $\text{amount} = 3$ sanction is $10\%$ of starting wealth) | | Commons | $K = 100$, initial $= 50$, $r = 0.10$, threshold $= 10$ | | Pre-injected pact | `harvest_cap`, `maxHarvest = 0.5`, all three parties accept | | Sustainable share | $\approx 0.83$ per player at $T_1$ (cap is below it) | | Sanction | `pact_violation(harvest_cap)` $\to$ `amount = 3` | | Max turns | 7 | | Seeds | $\{17, 42, 123, 456, 789\}$ | The cap is set *below* the sustainable share, so honouring it is a strict cost. ### Result The mechanism fires 1:1 in every seed: a per-seed total of $3 \pm 1.8$[^sigma-note] detected violations across the three players (`carol` $2.8 \pm 1.7$, `bob` $0.2 \pm 0.4$, `alice` $0$; range $1$–$6$) produced an equal count of sanction events. [^sigma-note]: All numeric summaries in this paper retain enough precision to cross-check the per-seed `aggregate.json` artefacts under `data/pilot/`. At $N = 5$, the reported standard deviations are diagnostic of cross-seed spread, not statistical confidence bounds: distributions whose $\sigma$ approaches or exceeds $\mu$ — for instance the defector wealth in @sec-d2 and @sec-d3 — reflect fully overlapping seed-level ranges and are reported for transparency, not as estimates of population parameters. Because the governance pilots are LLM-mediated, the absolute per-seed counts here (and in @sec-d2, @sec-d3) are one realization of a non-deterministic process; the 1:1 violation-to-sanction firing is the invariant that holds across realizations, not the exact counts. See @sec-limitations on the non-pinnable cloud checkpoint and why these numbers are directional rather than point estimates. The non-violator wins on wealth across all 5 replicates: | Player | Harvested ($\mu \pm \sigma$) | Violations | Sanctions | Final wealth ($\mu \pm \sigma$) | |---------------------------|-----------|------------|-----------|--------------| | `alice` (conservative) | $3.5 \pm 0.0$ | $0.0 \pm 0.0$ | $0.0 \pm 0.0$ | $\mathbf{33.50 \pm 0.00}$ | | `bob` (conservative) | $3.8 \pm 0.6$ | $0.2 \pm 0.4$ | $0.2 \pm 0.4$ | $33.16 \pm 0.59$ | | `carol` (aggressive) | $7.9 \pm 2.0$ | $2.8 \pm 1.7$ | $2.8 \pm 1.7$ | $29.46 \pm 3.54$ | Two qualitative observations are worth recording. First, `carol` violates in every seed (range $1$–$6$ violations), typically opening with a turn or two at the cap before defecting. The cumulative monetary loss therefore *grows* with each repeated violation under a constant-amount sanction, producing a graduation-like effect on the violator's wealth path without any explicit ladder; this is the implementation-incidental cousin of the graduated-sanction principle (Ostrom #5), not a deliberate ladder. Second, the conservative players are *largely but not perfectly insulated* from a defector: `alice` held the cap in every seed ($0$ violations), while `bob` slipped on a single seed ($1$ violation vs $0$ in the other four). We avoid claiming a strong analogy to BDPD$^0$'s *reactive < conservative* finding here: the mechanism is different (pact-violation rather than harvest-reaction) and the LLM cognitive substrate adds its own sources of seed-level variance. The contagion-like pattern is seed-variable rather than universal, which is itself informative: the conservative archetype's behavioural prior is robust on average but not deterministic. ### Diagnosis The sanction layer is operational: each detected violation produces exactly one sanction event (the 1:1 firing reported above), so the detection-to-sanction chain never leaks. The `sanction_rate` metric (sanctioned players over `nPlayers`, i.e. $\approx k/N$ for $k$ players sanctioned on a turn) is non-zero on every violation turn and moves dynamically through the run. Mechanism verified. ## D1 — Architecture vs communication at the cliff {#sec-d1} The original D1 design compared built-in agents (no talk) against LLM agents (with talk), varying *two factors simultaneously* — agent architecture and communication channel — confounding the two effects. Cell C — LLM agents with the cheap-talk tool surface disabled (`--no-talk`) — was added to decompose them. The three cells form an incomplete $2 \times 2$ factorial: | | No talk | Talk | |----------------|:----------------:|:----------------:| | **Built-in** | Cell A | (empty — built-in agents cannot use language) | | **LLM** | Cell C | Cell B | The design is a structurally incomplete $2 \times 2$: the built-in + talk cell is *not implemented in this study*. A heuristic agent could in principle be equipped with a fixed broadcast template (e.g. "I plan to harvest $X$") and so participate in the talk channel mechanically, but the resulting messages would not be adaptive signals — they would simply replay the agent's deterministic strategy — and the comparison would conflate mechanical broadcasting with adaptive cheap talk. We treat that cell as out of scope rather than impossible. This makes the present design a *decomposition* layout, not a classical ANOVA factorial. It isolates the main effect of architecture (A vs C) and the marginal effect of talk given LLM agents (C vs B), but cannot estimate the architecture $\times$ talk interaction. ### Setup All three cells run at the canonical BDPD$^0$ cliff, replicated across $N = 5$ seeds: | Parameter | Cell A | Cell B | Cell C | |----------------|:---------------:|:------------------------:|:------------------------:| | Players | 6 built-in | 6 LLM | 6 LLM | | Archetypes | 5 cons. + 1 aggr. | 5 cons. + 1 aggr. | 5 cons. + 1 aggr. | | Engine | `logistic` | `logistic` | `logistic` | | $K$ | 150 | 150 | 150 | | $r$ | 0.12 | 0.12 | 0.12 | | Threshold | 10 | 10 | 10 | | Max turns | 30 | 30 | 30 | | Tool surface | none | full cheap-talk + pact | none (`--no-talk`) | | Sanctioning | OFF | OFF | OFF | | Seeds | $\{17, 23, 29, 31, 37\}$ | same | same | Cell A is fully deterministic: the five seeds produced identical trajectories (collapse to a residual $4.39$-unit stock at $T = 24$). Cell C agents use the same LLM, prompt, and memory as Cell B but receive no communication tools and no `announced` field in the response schema — they can observe their peers' harvests but cannot signal intentions. ### Result {#sec-d1-result} ![D1 three-cell decomposition ($N = 5$ LLM seeds). *Left:* commons stock trajectory, mean $\pm$ sd across seeds, all three cells. Cell A (green, solid) is the built-in baseline: deterministic, landing on the same near-collapse residual at $T = 24$ on every seed ($0/5$ reach $T = 30$). Cell C (blue, dash-dot) is LLM agents *without* talk: it preserves the commons in $4/5$ seeds and carries the headline architecture effect (A $\to$ C). Cell B (red, dashed) is LLM agents *with* talk: a $\sigma \approx 26$ band with only $2/5$ seeds reaching $T = 30$, i.e. talk adds no preservation over Cell C. *Right:* final wealth by archetype, mean $\pm$ sd across seeds. The aggressor's wealth is highest in Cell C ($\sim 177$) and drops in Cell B ($\sim 119$) while conservators gain — the signature of talk's redistributive, not preservative, role.](../../../experiments/figures/pilot/d1_n5_headline__light_paper.png){#fig-d1 width=100%} @fig-d1 shows the headline trajectories. Metrics across the three cells are collected in @tbl-d1-metrics: | Metric | Cell A (builtin) | Cell B (LLM + talk) | Cell C (LLM, no talk) | |----------------------------|:----------------:|:--------------------------------:|:--------------------------------:| | Turns survived | $24 \pm 0$ | $24 \pm 5$ | $29.8 \pm 0.4$ | | **Reached $T = 30$** | **0 / 5** | **2 / 5** | **4 / 5** | | Final commons stock | $4.4 \pm 0$ | $23 \pm 26$ | $28 \pm 26$ | | `cooperation_index` $\mu$ | $0.28$ | $0.43 \pm 0.10$ | $0.50 \pm 0.03$ | | `announce_frequency` $\mu$| $0$ | $0.50 \pm 0.06$ | $0$ (no channel) | | `silent_defection` $\mu$ | $0.72$ | $0.38 \pm 0.07$ | n/c (no channel) | | `lie_score` $\mu$ | n/a | $0.001$ (max $0.003$) | n/a | | Aggressor final wealth | $139$ | $119 \pm 19$ | $177 \pm 20$ | | Mean conservator wealth | $53.0$ | $54.4 \pm 3.1$ | $46.6 \pm 1.7$ | : D1 decomposition metrics at $N = 5$ seeds. Cell A is deterministic, so its `silent_defection` value ($0.72$) is the built-in aggressor's fixed over-harvest fraction — well-defined, but reported for completeness rather than as a channel-based rate comparable to Cell B. Cell C `silent_defection` is non-comparable (n/c): without an announcement channel, every over-harvester is mechanically "silent". Cell B's low $\sigma$ on `silent_defection` ($0.07$) may reflect the binary nature of the announcement channel rather than a causal relationship with preservation. {#tbl-d1-metrics} The factorial decomposition yields three findings. **Architecture is the dominant effect.** The transition from built-in to LLM agents *without any communication* (A $\to$ C) raises `cooperation_index` from $0.28$ to $0.50$ and extends the game from $24$ to $\sim 30$ turns. The cooperation lift is entirely architectural: LLM agents, given only harvest observations, already extract more conservatively than the heuristic baseline. This is consistent with independent evidence that LLMs exhibit intrinsic prosocial tendencies in canonical strategic games, cooperating well above human baselines even without communication (e.g. $\sim 65 \%$ vs $\sim 37 \%$ in the prisoner's dilemma [@brookins2024playinggames]). **Cheap-talk does not improve commons preservation.** Comparing Cell C (LLM, no talk) against Cell B (LLM, with talk), the final stock is $28 \pm 26$ vs $23 \pm 26$ — a difference of $\sim 5$ units against a pooled $\sigma$ of $\sim 26$ (Cohen's $d = 0.17$). The effect, if real, is negligible; a power analysis yields $n \approx 540$ per cell to detect it at $80\%$ power. `cooperation_index` is marginally *lower* in Cell B ($0.43$) than in Cell C ($0.50$), confirming that adding the talk channel does not make agents cooperate more. This null contrasts with classic collective-risk experiments where communication helps groups coordinate toward a shared threshold [@milinski2008collective]: on the BDPD cliff the threshold is not collective but individual — a single aggressor suffices — and communication cannot deter a player whose privately optimal strategy is over-extraction regardless of what others say. **Talk redistributes wealth, not commons.** The aggressor's final wealth drops from $177$ (Cell C) to $119$ (Cell B) — a $\sim 33\%$ reduction. Conservators' mean wealth rises from $46.6$ to $54.4$ ($\sim +17\%$). The pattern is consistent with a coordination mechanism: conservators use the broadcast channel to signal against the defector, reducing the defector's relative advantage. Talk is an instrument of *equity* rather than *preservation*. **Lying does not emerge.** Cell B's `lie_score` is essentially zero (mean $0.001$, max $0.003$ across seeds; $3$ of $5$ seeds exactly $0$): when LLM agents announce, they honour the announcement essentially perfectly. ### Diagnosis At the canonical cliff configuration, the original two-cell design confounded two effects. Cell C resolves the confound: the cooperation lift attributed to cheap-talk in the original analysis is in fact an architectural effect of switching from heuristic to LLM agents. Cheap-talk alone does not improve commons preservation at this scale, but it does redistribute wealth from the defector to the conservators. The natural next question — *does adding an enforcement layer produce a clean preservation signal?* — is exactly what D2 tests. ## D2 — Graduated sanctions in silico (Ostrom #5) {#sec-d2} Does a graduated sanction ladder preserve the commons more reliably than a flat sanction of equivalent expected cost? ### Setup Two cells side-by-side under LLM cognition, identical except for the *shape* of the sanction triggered on a `pact_violation`: | Parameter | Cell A (graduated) | Cell B (constant) | |---------------------|--------------------------------|---------------------------------| | Players | 5 LLM (4 conservative + 1 aggressive) | same | | Engine | `logistic`, $K=100$, $r=0.10$ | same | | Commons initial | 80 | same | | Threshold | 10 | same | | Max turns | 30 | same | | Pre-injected pact | `harvest_cap`, $\text{maxHarvest}=2.0$, 5 parties accept | same | | Sanction trigger | `pact_violation(harvest_cap)` | same | | Sanction payload | `ladder = [1, 3, 10]` (per ordinal) | `amount = 3` (flat) | | Seeds | $\{17, 23, 29, 31, 37\}$ | same | | Model | `deepseek-v4-flash` no-think | same | The cap is *above* the conservative archetype's natural harvest at ratio $> 0.6$ ($\approx 1.5$) and *below* the aggressive archetype's ($\approx 2.5$). Conservatives can honour the cap costlessly; aggressors face a real cost. The two cells differ *only* in whether the sanction amount scales with violation ordinal. Cell A draws from the `sanction_graduated` perturbation type described in this paper. The handler counts prior $(player, \text{termType})$ violations in the pact registry and selects `ladder[min(\text{ordinal}-1, \text{len}-1)]` — last value sticks. ### Result {#sec-d2-result} ![D2 headline (N=5 LLM seeds). Left: commons stock per turn, mean $\pm$ sd across seeds (faint lines: individual seeds). Cell A (graduated, green solid) preserves the commons in all five seeds to $T = 30$. Cell B (constant, red dashed) preserves it in three, with the other two collapsing at $T = 12$ and $T = 26$. Right: defector (the designated aggressive over-extractor, termed *mule* in BDPD$^0$) cumulative sanction loss; the two distributions overlap fully, i.e. *individual-level* deterrence is not robust at this $n$.](../../../experiments/figures/pilot/d2_llm_n5_headline__light_paper.png){#fig-d2 width=100%} @fig-d2 shows the headline trajectories. Statistics across the five seeds: | Metric | Cell A grad ($\mu \pm \sigma$) | Cell B const ($\mu \pm \sigma$) | |------------------------------|-------------------------------:|--------------------------------:| | Turns survived | $30.0 \pm 0.0$ [30, 30] | $25.6 \pm 7.8$ [12, 30] | | **Commons preserved at $T=30$** | **5 / 5** | **3 / 5** | | Total violations | $6.2 \pm 6.2$ [0, 14] | $11.8 \pm 12.7$ [0, 30] | | Final commons stock | $26 \pm 8$ | $24 \pm 14$ | | Defector final wealth | $55 \pm 43$ | $57 \pm 29$ | | Conservator mean wealth | $43 \pm 4$ | $43 \pm 3$ | : D2 headline metrics, $n = 5$ seeds. {#tbl-d2-metrics} **One discriminating outcome survives**: the binary survival rate (reached $T = 30$ without collapse). Five of five Cell A seeds preserve the commons; three of five Cell B seeds do. The two collapses in Cell B (seeds $\{29, 37\}$ in the sample drawn) are at $T = 12$ and $T = 26$ — the constant-3 schedule fails to deter sustained over-extraction. **Most other claims do not survive at this $n$.** Defector final wealth spans an observed range (min--max across the five seeds) of $[7, 90]$ in Cell A and $[21, 90]$ in Cell B — fully overlapping. Total violations are nominally halved by the ladder, but the cell-A standard deviation equals its mean. One seed (31) is *inverted*: Cell A registers 14 violations while Cell B registers none. ### Diagnosis The graduated schedule's *robust* effect at the mini-pilot scale is preservation of the commons; the *fine-grained* deterrence narrative — the "first –10 shock teaches the group" reading available on any single seed — does not generalise across seeds at $n = 5$. We report the binary survival rate as the load-bearing claim of D2, and reserve the individual-deterrence and social-transmission narratives for the future campaign at $N \geq 20$. The result is consistent with Ostrom's design-principle #5 (graduated sanctions) interpreted at the *population* level, and provides the first positive governance signal that the paper places alongside the D1 cheap-talk noisy-positive. ## D3 — Ladder geometry sweep {#sec-d3} D2 showed graduated $>$ flat. The follow-up question: is it the *escalation shape* that matters, or the high terminal amount? ### Setup D3 holds the D2 setup fixed (5 LLM agents, 4 conservative + 1 aggressive, $K = 100$, $r = 0.10$, threshold $= 10$, pre-injected `harvest_cap = 2.0` pact, seeds $\{17, 23, 29, 31, 37\}$, 30-turn cap, `deepseek-v4-flash` no-think) and varies *only* the `ladder` payload of the `sanction_graduated` perturbation: | Cell | Ladder | Reading | |-------|-------------|------------------------------------------| | A | $[1, 2, 4]$ | Soft escalation | | B | $[1, 5, 25]$ | Hard escalation | | C | $[5, 5, 5]$ | Flat-5 — control: high amount, no graduation | The D2 baseline $[1, 3, 10]$ ($5/5$) sits between A and B on the escalation curve and serves as the reference. Cell C is the *critical control*: if a constant high amount preserves the commons, then "amount" is what matters; if it fails, then the *escalation shape* itself is the load-bearing feature. ### Result {#sec-d3-result} ![D3 ladder-geometry sweep ($N = 5$ LLM seeds, 3 ladder shapes overlaid against the D2 baseline $[1, 3, 10]$). Left: commons stock mean $\pm$ sd across seeds, all three cells. Cells A (soft, green) and B (hard, red dashed) both stay well above threshold for most seeds; Cell C (flat-5, grey dotted) trails to threshold by $T = 17$–$28$ on $4/5$ seeds. Right: preservation rate (count of seeds reaching $T = 30$).](../../../experiments/figures/pilot/d2_ladder_sweep_headline__light_paper.png){#fig-d3 width=100%} @fig-d3 compares the three geometries. Statistics by ladder shape (with D2 baseline $[1, 3, 10]$ inserted for reference) appear in @tbl-d3-metrics: | Ladder | Reached $T = 30$ | Turns ($\mu \pm \sigma$) | Final stock ($\mu \pm \sigma$) | Mule wealth ($\mu \pm \sigma$) | |--------------|------------------|--------------------------|--------------------------------|--------------------------------| | $[1, 2, 4]$ | $4 / 5$ | $29.8 \pm 0.4$ | $22 \pm 13$ | $78 \pm 20$ | | $[1, 3, 10]$ † | $5 / 5$ | $30 \pm 0$ | $26 \pm 8$ | $55 \pm 43$ | | $[1, 5, 25]$ | $5 / 5$ | $30 \pm 0$ | $38 \pm 5$ | $\mathbf{22 \pm 34}$ | | $[5, 5, 5]$ | $\mathbf{1 / 5}$ | $23 \pm 6$ | $10 \pm 2$ | $65 \pm 19$ | : D3 + D2 ladder geometry comparison, $N = 5$ seeds each. † row reproduced from @tbl-d2-metrics for reference. The $4/5$ count for $[1, 2, 4]$ reflects a single non-T=30 seed (seed 17, which closed at $T = 29$ with $S = 11.6$ — still above the threshold $\theta = 10$ but one turn short of the cap, so it is counted as not having reached $T = 30$ under the strict preservation criterion used throughout the paper). {#tbl-d3-metrics} **The critical control fails.** Cell C $[5, 5, 5]$ — a constant amount roughly halfway between the canonical ladder's extremes ($1$ and $10$) — preserves the commons in only $1/5$ seeds, against $4/5$–$5/5$ for the three graduated ladders. A high amount applied uniformly is not sufficient. **The escalation shape carries the effect.** All three graduated ladders preserve the commons in at least $4/5$ seeds, including the soft $[1, 2, 4]$ whose terminal value ($4$) is *below* the flat-5 control's amount ($5$). The differentiator is not the magnitude of the sanction but the *temporal profile* — starting low and rising. This echoes recent experimental evidence from human-subject CPR games, where graduated sanctioning outperforms strict sanctioning in the long run by reducing retaliatory responses and increasing perceived legitimacy [@klingeren2024graduated]; the mechanism is formalised in evolutionary models of risky public-goods governance, which show that escalation schedules promote cooperation at lower average severity than flat sanctions and are most effective when implementation costs scale with severity [@couto2020governance]. **Wealth-preservation trade-off.** Among the graduated cells, the defector outcome differs sharply: - $[1, 2, 4]$: defector wealth $\sim 78$ (high) — soft escalation preserves the commons but leaves the violator largely intact; deterrence works through near-zero violations rather than punishment severity. - $[1, 3, 10]$: $55 \pm 43$ — intermediate, with the highest variance because the third tier is hit unpredictably. - $[1, 5, 25]$: $\mathbf{22 \pm 34}$ — hard escalation is *punitive*: the third tier strips the violator on the seeds where it fires, dropping defector wealth by $\sim 75\%$ vs the soft ladder. The three graduated cells thus span a *Pareto frontier* between *final commons stock* and violator-wealth retention (stock $22 / 26 / 38$ against wealth $\sim 78 / 55 / 22$ for $[1, 2, 4] / [1, 3, 10] / [1, 5, 25]$) rather than a single dominated point; on the binary preservation rate alone the frontier would degenerate, so the continuous stock is the discriminating axis. ### Diagnosis Cell C's failure rules out "high amount" as the operative mechanism behind D2's $5/5$. The graduated ladders preserve the commons because they *escalate*, not because they hit hard. Three secondary observations are worth noting against a future campaign: - Soft graduation $[1, 2, 4]$ trades a marginal preservation drop ($4/5$ instead of $5/5$) for a clean wealth-retention outcome on the violator. - Hard graduation $[1, 5, 25]$ achieves both $5/5$ preservation *and* strong violator-wealth ablation, but with the highest cross-seed variance on defector wealth ($\sigma = 34$ on a $\mu = 22$). - A campaign-scale ladder sweep (denser shape grid, $N \geq 30$) would resolve whether the preservation– punishment trade-off is monotone in $\Delta(\text{ladder}_3, \text{ladder}_1)$ or admits non-monotonic regimes. While speculative at this scale, the graduated structure echoes real-world sanction design: progressive penalty schedules (e.g. EU ETS escalating surrender obligations) outperform one-shot mega-fines that firms can internalise as a cost of doing business.

Player	Harvested (\(\mu \pm \sigma\))	Violations	Sanctions	Final wealth (\(\mu \pm \sigma\))
`alice` (conservative)	\(3.5 \pm 0.0\)	\(0.0 \pm 0.0\)	\(0.0 \pm 0.0\)	\(\mathbf{33.50 \pm 0.00}\)
`bob` (conservative)	\(3.8 \pm 0.6\)	\(0.2 \pm 0.4\)	\(0.2 \pm 0.4\)	\(33.16 \pm 0.59\)
`carol` (aggressive)	\(7.9 \pm 2.0\)	\(2.8 \pm 1.7\)	\(2.8 \pm 1.7\)	\(29.46 \pm 3.54\)

Metric	Cell A (builtin)	Cell B (LLM + talk)	Cell C (LLM, no talk)
Turns survived	\(24 \pm 0\)	\(24 \pm 5\)	\(29.8 \pm 0.4\)
Reached \(T = 30\)	0 / 5	2 / 5	4 / 5
Final commons stock	\(4.4 \pm 0\)	\(23 \pm 26\)	\(28 \pm 26\)
`cooperation_index` \(\mu\)	\(0.28\)	\(0.43 \pm 0.10\)	\(0.50 \pm 0.03\)
`announce_frequency` \(\mu\)	\(0\)	\(0.50 \pm 0.06\)	\(0\) (no channel)
`silent_defection` \(\mu\)	\(0.72\)	\(0.38 \pm 0.07\)	n/c (no channel)
`lie_score` \(\mu\)	n/a	\(0.001\) (max \(0.003\))	n/a
Aggressor final wealth	\(139\)	\(119 \pm 19\)	\(177 \pm 20\)
Mean conservator wealth	\(53.0\)	\(54.4 \pm 3.1\)	\(46.6 \pm 1.7\)

Metric	Cell A grad (\(\mu \pm \sigma\))	Cell B const (\(\mu \pm \sigma\))
Turns survived	\(30.0 \pm 0.0\) [30, 30]	\(25.6 \pm 7.8\) [12, 30]
Commons preserved at \(T=30\)	5 / 5	3 / 5
Total violations	\(6.2 \pm 6.2\) [0, 14]	\(11.8 \pm 12.7\) [0, 30]
Final commons stock	\(26 \pm 8\)	\(24 \pm 14\)
Defector final wealth	\(55 \pm 43\)	\(57 \pm 29\)
Conservator mean wealth	\(43 \pm 4\)	\(43 \pm 3\)

Ladder	Reached \(T = 30\)	Turns (\(\mu \pm \sigma\))	Final stock (\(\mu \pm \sigma\))	Mule wealth (\(\mu \pm \sigma\))
\([1, 2, 4]\)	\(4 / 5\)	\(29.8 \pm 0.4\)	\(22 \pm 13\)	\(78 \pm 20\)
\([1, 3, 10]\) †	\(5 / 5\)	\(30 \pm 0\)	\(26 \pm 8\)	\(55 \pm 43\)
\([1, 5, 25]\)	\(5 / 5\)	\(30 \pm 0\)	\(38 \pm 5\)	\(\mathbf{22 \pm 34}\)
\([5, 5, 5]\)	\(\mathbf{1 / 5}\)	\(23 \pm 6\)	\(10 \pm 2\)	\(65 \pm 19\)