What happens to a population of agents when it is told its own collective state — and what happens when that description is false?
Narcissus is a controlled, fully reproducible laboratory for recursive self-model feedback in evolving multi-agent networks. Temporary agents are born, cooperate, compete, reproduce and die, forming an adaptive network G(t). A global observer periodically compresses the macrostate — fragmentation, degree concentration, cooperation, inequality, turnover — into a self-model S(t) and, depending on the experimental condition, broadcasts it back to the agents accurately, systematically falsified, replayed from another run, or as matched-range random noise:
local actions → global condition → measurement → self-model → broadcast → changed local actions
Each agent carries a heritable global sensitivity trait γ that scales how strongly the broadcast moves its action propensities. Nothing in the rules refers to whether the broadcast is true.
Evidence base: 927 core runs + 1,000 architectural-control runs + 1,200 ecology-ensemble runs = 3,127 (as reported in the manuscript), all deterministic and paired by seed. Four outcome families were pre-specified before the first campaign; everything else is labelled exploratory.
Measurement alone is causally inert. The observed-but-blind condition is trajectory-identical to no-observer under paired seeds — every per-seed difference exactly zero, on every outcome, twice replicated. Only the broadcast has causal power. (The engine computes S(t) under the no-feedback baseline too, for logging, so this doubles as a strict observer-side-effect invariance check.)
Apparent "story pull" is an artifact — and that is the methodological finding. A natural self-fulfilling-prophecy statistic registers strong, replicated apparent attraction of the macrostate toward false and replayed self-models (raw hierarchy: replay > inverted lie > noise). But a passive counterfactual — scoring untreated paired-seed twins against matched reference signals — fully accounts for it. Untreated worlds "move toward" the references more than treated worlds do (passive medians 0.012 / 0.030 / 0.007 vs actual 0.008 / 0.024 / 0.001), the per-condition gap ΔP = P_actual − P_passive is uniformly negative, and adjusted between-condition contrasts are null in both campaigns (F vs N: p = 0.084 harsh, p = 0.63 flagship). There is no evidence of content-specific attraction toward broadcast content. A three-line mean-reversion argument shows why this class of directional metric can read positive with zero causal feedback. Direct caution for empirical performativity claims — scripts/passive_null_checks.py.
What broadcasts do change is behavior and structure, and the lie–response pair decides which lies come true. Under corrective agents an alarmist lie is self-defeating and a flattering lie is behaviorally inert; false and noise broadcasts densify the network and reduce hub concentration (the densification arm under truthful feedback is the one claim the ecology ensemble does not sustain — see below). Under conformist agents the taxonomy flips: the alarmist lie becomes catastrophically self-fulfilling (fragmentation ×10), the flattering lie becomes benevolently self-fulfilling, and even noise mobilizes cooperation. Formally, self-fulfillment is a property of the composition R∘B (response rule ∘ broadcast map), not of the message alone. First-order response directions follow from the rules by construction and are not claimed as discoveries.
Truthful feedback doubles costly cooperation — 0.397 vs 0.179 baseline (paired Δmedian +0.200, r = 1.00), monotone in gain, replicated under harsh shock and at 2× scale. And one pre-specified null, twice replicated: no feedback effect on post-shock recovery time in either main campaign, in any condition, even at 40% hub removal (every paired Δmedian exactly 0, all p > 0.22). One contrary lead is reported rather than buried — at 2× scale the inverted lie delayed recovery in every non-tied pair (+10 steps, r = 1.00), but with n = 8 that is the smallest p the test can return (0.0625) and it does not replicate at base scale.
Attention to the self-model declines under consequential broadcasts. γ is heritable and mutated; its population mean falls across ~20 generations of lineage depth, ordered false > noise > truth > silence, with a clean dose-response in feedback gain. Nobody programmed that ordering — and unlike models where agents update trust from observed accuracy, here nothing references reliability: trust is not updated, it evolves.
Two follow-ups keep that result honest:
- What organizes it. Veracity alone does not — the utopia lie is false yet produces no decline, while truthful feedback declines at high gain. The categorical ordering compresses into one relationship with the broadcast-implied corrective-drive intensity I = g·⟨Σ f_a(b)⟩ (Spearman ρ = −0.99 across 15 sweep cells, −0.83 at run level). This is descriptive, not causal mediation: I omits the per-agent factor γ and is computed from already-feedback-affected trajectories —
scripts/attention_cost.py. - What it is not. Two asymmetries in the architecture could in principle manufacture the pattern, and each was rerun as its own 300-run sweep —
scripts/reproduction_neutral_check.py. (a) Reproductive opportunity. Feedback adds weight only to non-reproductive actions, so after normalization a higher-γ agent mechanically has a lower probability of selecting reproduce — and I is exactly the quantity governing that penalty. A reproduction-neutral variant holding that selection probability exactly invariant (verified spread 0.00000 across γ) reproduces the decline almost perfectly: median retention 98%, no cell shifting significantly, ρ = −0.98 persisting, and truth declining more under the control. (b) γ-in-pruning. Hub-targeted pruning fires with probability γ_i rather than γ_i·g — a second, differently scaled channel acting straight on structure. Fixing it at 0.5 for every agent: median retention 100%, and the intensity correlation strengthens (ρ = −0.993 → −1.000); one cell of fifteen shifts significantly (N@g0.8, p = 0.033), an attenuation that still retains 77%. Selection on γ is ecological, not an artifact of either channel. (c) The rule form itself. Swapping the entire response function for the structurally unrelated conformist mapping, γ̄ still falls in every broadcast condition (paired Δmedian −0.14 to −0.57, all p ≤ 0.022) — so the phenomenon is not an artifact of the corrective rule form, the single most-repeated criticism of this work. Reported with its negative half: the ordering, and the I that summarises it, do not transfer across regimes (ρ = +0.10, p = 0.87) —scripts/rule_form_check.py. (d) γ as the only exit. (a)–(c) all keep the response mapping fixed, so lowering γ stays the only way to disengage. Making the polarity and strength ρ ∈ [−2,2] of each action channel heritable — ρ = 1 reproducing the hand-written rule bit-identically, ρ = 0 ignoring it, ρ < 0 reversing it — opens a second route, and γ̄ still declines (vs A, n = 100: C −0.125, F −0.222, N −0.212; all p < 1e-5). Freeing ρ attenuates the decline under false and noise feedback but not under truth, so populations use both routes exactly where disengagement pays —scripts/policy_campaign.py.
Full statistics and caveats: campaigns/FINDINGS.md.
| Condition | Observer | Agents receive | Role |
|---|---|---|---|
| A — Local only | off | nothing | baseline |
| B — Observed, blind | on | nothing | measurement control |
| C — True feedback | on | accurate S(t) | main treatment |
| F — False feedback | on | distorted S(t): invert / crisis / utopia | reflexivity probe |
| N — Noise feedback | on | uniform random, matched ranges | stimulation control |
| R — Replayed self-model | on | another run's genuine S(t) | structure control |
Ecological robustness — 1,200 further runs. The standing objection to this work is that it lives in one ecology. Answered with a pre-registered randomized ensemble: 24 ecologies drawn by perturbing six ecological parameters ±25% (resource inflow, capacity, reproduction cost, metabolism, link cost, mortality), screened for viability using only the no-broadcast baseline and criteria frozen before any broadcast condition ran — so no ecology could be admitted or dropped for showing the desired result. All 24 passed, with room to spare. Then A/B/C/F/N × 10 paired seeds in each.
The three central results replicate in every ecology: cooperation up under truth (24/24, median +0.184), attention falling under the lie (24/24, −0.396) and under noise (24/24, −0.258), and the observed-but-blind identity (24/24, every per-seed difference exactly zero). The pre-specified recovery null holds in 24/24 for F and N and 22/24 for C. The dose-ordering F ≤ N ≤ C ≤ A holds exactly in 21/24, median rank correlation +1.00.
One claim does not survive, and is reported rather than dropped: densification
under truthful feedback is significant in 1 of 24 and correct-signed in 16,
against 24/24 on sign for both distortions — so the claim is false and noise
broadcasts densify the network, not broadcasts densify the network. Scope
stated plainly: ±25% gives per-ecology spreads of 2.5× in mean degree, 2.2× in
cooperation, 1.9× in population — evidence of local ecological robustness, not
of arbitrary-ecology generality — scripts/ecology_ensemble.py.
Multiplicity: over the eight point-p contrasts of the paper's Table 3, both Benjamini-Hochberg and the stricter Holm-Bonferroni correction leave every significance decision unchanged (6 of 8 either way). Enlarged to a deliberately hostile family of all 74 paired contrasts the paper reports, BH still leaves all eight unchanged; Holm demotes exactly one — fragmentation (flagship) F vs A, the weakest at p = 9.5e-4. Reported rather than scoped away — scripts/multiplicity_check.py.
Paired seeds across conditions; standardized hub-removal shocks (10 hubs mild, top 40% harsh, at t = 2000 — t = 1500 in the 2× scale check); paired Wilcoxon signed-rank as the primary analysis with tie-corrected matched-pairs rank-biserial r and bootstrap CIs (Mann–Whitney U + Cliff's δ is a secondary view and does not agree everywhere — all inferential claims follow the paired analysis); passive-counterfactual nulls for the story-pull statistic; a dedicated signal-RNG stream so constructing the noise signal never advances the behavioral PRNG; robustness across feedback gains (0.2–1.6), two shock severities, 2× system scale, and two response regimes (corrective / conformist).
pip install -r requirements-lock.txt # exact versions used for the reported runs
python scripts/replay_check.py # seed-replay determinism, cross-platform
python scripts/validate_metrics.py # observer metrics vs closed-form cases
python -m pytest tests/ -q # 13 tests: determinism, metrics, viability
python run.py --condition F --distortion invert --steps 2000 --seed 7
python scripts/dashboard.py runs/F_s7_n2000 # self-contained interactive dashboard
python scripts/demo.py # one-command live-demo kitCampaigns and analyses (raw runs/ are gitignored — either unpack the release
assets into campaigns/, or regenerate with the commands below):
# core campaigns
python scripts/campaign.py --seeds 50 --shock-step 2000 --out campaigns/flagship
python scripts/campaign.py --seeds 30 --shock-fraction 0.4 --out campaigns/harsh_shock
python scripts/replay_control.py # condition R + 15 source trajectories
python scripts/size_robustness.py # 2x scale check
python scripts/analyze_campaign.py campaigns/<name>
# architectural controls, 300 runs each (Sect. 5.5)
for G in 0.2 0.8 1.6; do python scripts/campaign.py --out campaigns/rn_g$G --seeds 20 \
--steps 4000 --shock-step 2000 --gain $G --shock-fraction 0.4 \
--conditions "C,F:invert,F:crisis,F:utopia,N" --reproduction-neutral; done
for G in 0.2 0.8 1.6; do python scripts/campaign.py --out campaigns/pgf_g$G --seeds 20 \
--steps 4000 --shock-step 2000 --gain $G --shock-fraction 0.4 \
--conditions "C,F:invert,F:crisis,F:utopia,N" --pruning-gamma-free; done
# analyses reported in the paper
python scripts/passive_null_checks.py # passive counterfactual (Sect. 5.2)
python scripts/reproduction_neutral_check.py # reproductive-opportunity control (Sect. 5.5)
PO_VARIANT=pgf python scripts/reproduction_neutral_check.py # gamma-free-pruning control (Sect. 5.5)
python scripts/attention_cost.py # corrective-drive intensity vs evolved attention
python scripts/reviewer_checks.py # source-dependence, P>0, eps-sensitivity, activation
python scripts/config_model_null.py # ER + degree-preserving clustering nulls
python scripts/multiplicity_check.py # BH + Holm over the Table 3 contrasts
python scripts/rule_form_check.py # does the decline survive swapping the rule set?
python scripts/selection_mechanism.py # what the gamma decline is NOT (fecundity, shock)
python scripts/sweep_figure.py campaigns/sweep_g0.2 campaigns/sweep_g0.8 campaigns/sweep_g1.6
python scripts/paper_figures.py # redraw Figs. 2-3 at printed size
# ecological robustness: 24 ecologies, viability frozen before any treatment ran
python scripts/ecology_ensemble.py --validate # reproduces harsh_shock 16/16 to 1e-10
python scripts/ecology_ensemble.py --screen # stage 1: baseline only, then STOP and read
python scripts/ecology_ensemble.py --run # stage 2: treatments in the frozen viable set
python scripts/ecology_ensemble.py --merge # fold multi-machine checkpoints, cross-check hashes
python scripts/ecology_ensemble.py --analyze # stage 3: claims counted across ecologies--run is resumable and splits across machines: each writes its own
checkpoint (--checkpoint) and reads every checkpoint present, so two
machines never repeat each other's work. Any run computed twice becomes a free
cross-platform check — --merge compares state hashes and refuses to merge on
disagreement. The reported 1,200-run ensemble was produced this way across
x86_64/Python 3.11/networkx 3.6.1 and aarch64/Python 3.10/networkx 3.4.2, with
31 overlapping runs agreeing bit-for-bit.
Every run is deterministic given (config, seed); state hashes verify replay across machines and operating systems. One PRNG drives all behavioral choices and a separate stream generates stochastic broadcast signals, so constructing the noise signal never advances the behavioral PRNG — with both control flags off the engine reproduces every stored campaign hash bit-for-bit.
A Network and Its Reflection: What True, False, and Noise Self-Model Broadcasts Do and Do Not Change in an Evolving Multi-Agent Network — under submission to Complex Networks 2026. Sources and PDF in paper/; research plan and original proposal in docs/. The tag cn2026-submission marks the exact state the paper describes; every run regenerates deterministically from the pinned configuration and seed (see Reproduce everything above).
Active research. Criticism, replication attempts, and issues welcome — this project has already retracted one of its own headline results after a stronger control (passive_null_checks.py) showed it was explained by intrinsic dynamics, and retained another after two exact mechanistic controls (reproduction_neutral_check.py) failed to remove it.
MIT