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Communication Shapes Collective Inference in Self-Adapting LLM Societies: Evidence from Mafia
Haonan Huang, Joey Xiao
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Abstract
Abstract:When does communication help a group identify hidden adversaries, and how does its value change as the group adapts? In Mafia, an informed minority hides inside an uninformed majority whose only evidence is open play. The zero-information game, where each day's vote eliminates a random player, is exactly solved and scores every society; matched-casting comparisons between protocols identify the effect of communication. Societies of 8-100 claude-haiku-4-5 agents (7,416 analyzed games, 1.9M model calls) adapt by rewriting and inheriting private strategy notes. Simultaneous broadcast improves adversary identification over silence in all nine compositions tested (8-46 players). Turn-taking removes most of this advantage; its voting landslides are as frequent as broadcast's but land on mafia near chance (1.08x versus 2.53x). At 70 players, agents reading eight statements per day identify adversaries worse than silent ones, and limited talk is worth less than at 46 players. Adaptation is fast but need not help. In their first broadcast games, citizens announce their role far more often than mafia (91% vs. 30%) and first-day votes find mafia at three times chance; within two generations citizens stop announcing and the cue fades, a change the inherited notes carry. In controlled redeployments at 16 players, societies carrying sixty generations of their own notes score below societies with none. Communication shapes both collective inference and the signals it depends on, so a protocol's value must be measured together with the adaptation that changes those signals.
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- Source: https://arxiv.org/abs/2610.05041v1
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Communication Shapes Collective Inference in Self-Adapting LLM Societies: Evidence from Mafia Haonan Huang Affiliation: Princeton University, Princeton, NJ, USA and Joey Xiao Affiliation: New York University, New York, NY, USA © none Abstract. When does communication help a group identify hidden adversaries, and how does its value change as the group adapts? In Mafia, an informed minority hides inside an uninformed majority whose only evidence is open play. The zero-information game, where each day’s vote eliminates a random player, is exactly solved and scores every society; matched-casting comparisons between protocols identify the effect of communication. Societies of 8–100 claude-haiku-4-5 agents (7,416 analyzed games, 1.9 M model calls) adapt by rewriting and inheriting private strategy notes. Simultaneous broadcast improves adversary identification over silence in all nine compositions tested (8–46 players). Turn-taking removes most of this advantage; its voting landslides are as frequent as broadcast’s but land on mafia near chance (1.08×1.08× versus 2.53×2.53×). At 70 players, agents reading eight statements per day identify adversaries worse than silent ones, and limited talk is worth less than at 46 players. Adaptation is fast but need not help. In their first broadcast games, citizens announce their role far more often than mafia (91% vs. 30%) and first-day votes find mafia at three times chance; within two generations citizens stop announcing and the cue fades, a change the inherited notes carry. In controlled redeployments at 16 players, societies carrying sixty generations of their own notes score below societies with none. Communication shapes both collective inference and the signals it depends on, so a protocol’s value must be measured together with the adaptation that changes those signals. Keywords: LLM agents; multi-agent communication; social deduction; Mafia; hidden-role games; exact baselines; cultural adaptation; collective dynamics 1. Introduction When does communication help a group identify hidden adversaries — and what does a society’s own accumulated experience do to that ability? Multi-agent LLM systems are increasingly built on the premise that agents which talk (Du et al., 2024; Chan et al., 2024) and agents which remember (Park et al., 2023; Shinn et al., 2023) do better than agents which do not; communication value is usually reported as an improvement over a no-communication ablation (Lowe et al., 2019; Piatti et al., 2024; O’Gara, 2023), with neither arm on a common scale. And “helps” is one-sided: the same channel can serve the hunted minority as well as the majority hunting it. The quantitative question is what each way of organizing communication does to the balance between the two. The hidden-role game Mafia supports a sharper design. An uninformed majority (town) faces an informed minority (mafia) that eliminates one citizen every night; each day the whole society eliminates one player by plurality vote. The game’s mathematics is unusually complete: Braverman, Etesami and Mossel (Braverman et al., 2008) showed that a fair game needs a mafia of order the square root of the population (revisited by Yao (Yao, 2008)), and Migdał (Migdał, 2010) solved the zero-information game (day votes blind, night kills unrestricted) in closed form, a line that remains active (Stock and da Silva, 2026; Tamashiro, 2026; Knight, 2026); the nearest analytic treatment of LLM Mafia play is a capability model for a four-player, single-day variant (Costa and Vicente, 2026). We use the zero-information process as a fixed reference: Section 3 lays out its complete phenomenology, exactly and by simulation, and every LLM society is measured as a per-elimination tilt θ against it — while the value of communication itself is identified as the paired difference between protocols on matched castings, never as a departure from the reference, which non-linguistic channels also move (Section 2). On that ruler we place societies of claude-haiku-4-5 agents at (n,m)∈(8,2),(12,3),(16,1..5),(n,m)∈\(8,2),(12,3),(16,1..5), (26,4),(46,5),(70,6),(100,7)(26,4),(46,5),(70,6),(100,7)\, which adapt across generations by rewriting private strategy notes after each game — the only cross-game channel; all strategy content is agent-authored. Communication is manipulated three ways: the protocol (simultaneous broadcast; sequential turn-taking; silence; a private-planning turn), the bandwidth k (each player reads a private uniform sample of k statements per day), and an informed detective. Frozen evaluations redeploy fixed notes on fresh castings, separating what was learned from the protocol it is deployed into. The paper reads the record in three layers, each with its own standard of evidence: statics (paired protocol contrasts on matched castings), dynamics (time-series tests against surrogate nulls, and frozen redeployments that intervene on the notes), and behavior (associations in the game traces). Contributions. (1) Measurement: every lynch is scored against the exact blind-chance rate (a logistic model with a known offset; a valid partial likelihood because night kills remove only citizens), over 7,416 games whose records are re-hashed and audited; the reference process is laid out exactly (Sections 2–4). (2) Statics: broadcast talk shifts the balance toward the majority, over silence, in 9 of 9 tested compositions; turn-taking erases most of the shift; blank notes score above every evolved family in frozen broadcast redeployment at one composition (resolved for five of six); talk at eight or twelve statements per day is worth less at 70 players than at 46 (one family per arm), and full broadcast does not fit the context window at 100 (Section 5). (3) Dynamics: the generation-1 tell and its collapse, shown by frozen cross-deployment to travel with the inherited notes while written advice mostly lags it (median first statement at generation 19, against a collapse at generation 2); and only broadcast societies show excess slow fluctuation and family individuation, over outcomes with no detected trend (Section 6). (4) Behavior (associations in the traces): lying is rare, and mafia who claim citizenship are lynched more, not less; claims mark citizens and draw the night kill; turn-taking herds statements, not ballots, into cascades, and its landslides, as frequent as broadcast’s, land on mafia near chance — about two-fifths of its accuracy deficit (Section 7). 2. Game Rules and Measurement Pinned mechanics. n players, m of them mafia; the mafia know each other, citizens know only their own role. Each day, every living player submits one public statement (≤ 80 words) and then votes; the plurality choice is eliminated (ties uniform); we call the day elimination a lynch throughout. How statements are composed and delivered (all at once, one speaker at a time, or not at all) is the manipulated protocol (Section 4); voting is always simultaneous, and the eliminated player’s faction and the full who-voted-whom record are published at the start of the next day. Each night the mafia eliminate one citizen (rotating chooser). Town wins by eliminating every mafioso; mafia win when they strictly outnumber the remaining citizens. One elimination per phase is mandatory, so game length is bounded. Measurement. Write ntn_t and mtm_t for the living players and living mafia when day t’s lynch is cast. A lynch blind to roles hits mafia with probability exactly mt/ntm_t/n_t — the living mafia’s population share. That blind process is the zero-information reference: its mafia win probability w(n,m)w(n,m) is known in closed form (Migdał, 2010) (e.g. w(16,3)=0.576w(16,3)=0.576, w(100,7)=0.530w(100,7)=0.530), and Section 3 lays out how it plays. Against it, every recorded lynch is one Bernoulli observation with logitqt=logit(mt/nt)+θlogitq_t=logit(m_t/n_t)+θ: the tilt θ measures how far a society’s lynches deviate from blind chance — by convention positive toward town (mafia found faster), negative toward the informed minority. θ θ maximizes ∑thtlogqt+(1−ht)log(1−qt) _th_t q_t+(1-h_t) (1-q_t) over an arm’s lynches; because night kills remove only citizens, (nt,mt)(n_t,m_t) and the game’s end are functions of the lynch outcomes, so if the hit probability given the past is qtq_t this is the exact likelihood of the lynch sequence; otherwise θ θ is the tilt at which observed and tilted-chance hits balance. All CIs are 95% percentile bootstraps resampling games (B=2000B=2000, fixed seeds); contrasts between arms sharing casting seeds are paired at the casting level. “Resolved” means the CI of a difference excludes 0; Section 5 applies no multiplicity correction (the nine headline contrasts survive Holm and Benjamini--Hochberg; supplement)11 1 “Supplement” refers to the supplementary material of the conference submission (verification detail, robustness tables, extended figures); it is omitted from this preprint and is available from the authors., Section 6 corrects within test families; an additive-risk estimator agrees on the headline contrasts (supplement). A generation-block bootstrap leaves the headline contrasts unchanged and widens the scale intervals of Section 5.4 by 17–32% (supplement). Identification. The reference is a fixed mechanical ruler, not a claim about what any LLM society would do absent language: silent societies sit below it in six cells (Section 5.1), consistent with the remaining channels moving elimination too: the published ballot record, which lets an informed minority coordinate ballots (Wang, 2026), and its choice of night victims (the interventions that would separate the two were not run). No single-arm tilt is therefore read as “the value of words”: the estimand throughout is the paired protocol contrast on matched castings. The game engine is verified against the exact theory (8 zero-information cells, 9 checks, max |z||z| 1.43; a count-level chain MC passes 52 more; supplement). 3. The Zero-Information Game, Simulated Before any language model plays, we lay out what the reference society does. Each law below is computed exactly by dynamic programming, agrees with Migdał’s closed form (Migdał, 2010) on all 1,767 even-n states (n≤120n≤ 120), and is reproduced by 2.1×1072.1×10^7 independently coded Monte-Carlo games (max |z||z| 1.86 for win probabilities, 2.97 over all laws; supplement). The surface and its limit. At fixed density x=m/nx=m/ n the mafia win probability declines slowly with n toward a limit curve: taking n→∞n→∞ in the even-n closed form of (Migdał, 2010) gives w(n,xn)→2Φ(x)−1w(n,x n)→ 2 (x)-1, with first correction +x2φ(x)/n+x^2 (x)/ n (our term-by-term expansion; derivation in the supplement; it differs from the parity-indexed profiles (Tamashiro, 2026) proves under weak-majority stopping). The dilute asymptotic (Migdał, 2010, Eq. 24) is this limit’s linear term, and all corpus sizes collapse onto the curve (plotted in the supplement). The fair line. The n n scaling of the fair mafia count is classical (Braverman et al., 2008; Yao, 2008); the exact even-n line m∗(n)m^*(n) — where w crosses 12 12 — runs at m∗/n=0.646m^*/ n=0.646–0.6570.657 over our sizes (≈0.65n≈ 0.65 n), and tends to Φ−1(3/4)=0.6745 ^-1(3/4)=0.6745 as 0.6745−0.2275/n0.6745-0.2275/ n; the dilute root 0.627n0.627 n (Migdał, 2010, Eq. 25), which (Migdał, 2010) argues is exact for even n, understates it at every n. The measured fair-line shifts of Section 5.1 are read against these exact values. How a null game unfolds. With τ=2t/nτ=2t/n the fraction of the maximal span elapsed and M the initial mafia count, the mean mafia count tracks Migdał’s law mt≈M1−τm_t≈ M 1-τ (Migdał, 2010, Eq. 21) (within 0.2–1.5% at mid-game) around a widening fan (supplement), and the game is decided late: mafia wins are possible only in the last m days, and at the five simulated sizes expected length is 91–97% of the n/2n/2 bound and 97–98% of games end in those days. One structural fact holds for any lynch rule, hence for every LLM game in this paper: with even n the night kill never ends the game, so every game ends at a day lynch — the lynch sequence on which our partial likelihood conditions carries every decision. From per-lynch tilt to win rate. The tilted process maps any θ to a town win rate (Fig. 1), and its sensitivity grows with size at similar density: dtown/dθd\,town/dθ at θ=0θ=0 is 0.49 at (16,3)(16,3), 0.66 at (46,5)(46,5), 0.79 at (100,7)(100,7), because a fixed per-lynch edge compounds over ∼n/2 n/2 lynches. Because the map’s slope grows with n, a constant per-lynch edge would buy more wins in larger societies; the decline reported in Section 5.4 is in the per-lynch tilt itself, before any mapping to wins. Three stacked plots, one each for 16, 46 and 70 players, show how the town's chance of winning rises with the lynching tilt in the exact zero-information game, with each measured society marked on its curve and its observed win rate beside it; at 70 players the talking societies win more often than their tilt predicts. Figure 1. The tilt map: town win rate vs. per-lynch tilt θ at three sizes, with measured arms marked (filled: tilt prediction, 95% CI; open: observed town rate, Wilson 95%). The slope at θ=0θ=0 grows with n; the reference surface and trajectories are in the supplement.Three stacked plots, one each for 16, 46 and 70 players, show how the town's chance of winning rises with the lynching tilt in the exact zero-information game, with each measured society marked on its curve and its observed win rate beside it; at 70 players the talking societies win more often than their tilt predicts. 4. Societies, Adaptation, Harness Agents (design schematic in the supplement). Every seat runs claude-haiku-4-5(Anthropic, 2025) (snapshot 20251001; extended thinking disabled, temperature 1.0, decoding contract pinned and verified per request), living in its own session for the length of a game, whose growing transcript is the agent’s memory within that game: one plain reasoning-and-reply loop, no compaction or summarization, driven by a Python orchestrator that pins and archives every request at bare-API equivalence (detail in the supplement); between games, the notes are the only channel. Design schematic: the three statement protocols, and the generational loop in which each agent is debriefed after a game and rewrites its strategy notes for the next generation, with a dashed branch where notes are frozen and redeployed. Figure 2. The manipulated protocols (top) and the adaptation loop (bottom): after each game every agent rewrites its strategy notes, served to the lineage’s next game with roles re-randomized; frozen evaluations redeploy fixed notes with learning off. Chains: 60 generations up to (46,5)(46,5), 40 at (70,6)(70,6), 20 for the twins.Design schematic: the three statement protocols, and the generational loop in which each agent is debriefed after a game and rewrites its strategy notes for the next generation, with a dashed branch where notes are frozen and redeployed. One chain with a stronger mafia (claude-sonnet-5) in a Haiku town is the only capability probe: town win rate down 0.22 [0.02, 0.42] vs Haiku mafia, tilt still above the reference (+0.43+0.43 [-0.01, +0.81]); 30 games, not a model-dependence test. Agents reply with one JSON object per turn and may keep a private note (≤ 40 words); malformed replies draw bounded corrections and can never stall the game — a still-failing statement simply publishes nothing (full fallback rules in the supplement). Protocols. Broadcast: statements composed simultaneously, then served. Sequential: one speaker at a time around a circle with a uniformly random start seat and direction each day (not a uniform random permutation); each speaker sees today’s earlier statements. Silent (k=0k=0): no statement phase; private planning replaces the statement slot by an unserved analysis turn (used only in a control). Bandwidth. At finite k, each player receives a private uniform sample of k of the other players’ statements, in both phases; draws come from a seeded per-(day, seat) stream and are recorded. Adaptation and freezing. Societies play repeated games in lineages: after each game every agent sees the outcome, the full role reveal and the public record it missed, then rewrites its strategy notes, a verbal-reflection loop inherited across games (Shinn et al., 2023) (400 words requested, not enforced; realized per-chain means 430–1,054), served back next game with roles re-randomized. This is cultural transmission rather than selection (Perez et al., 2025): lineages accumulate and inherit experience; nothing is selected, scored or recombined (cf. LLM generations with selection of top performers (Vallinder and Hughes, 2025)). A cell is one (n,m)×(n,m)×protocol condition; each cell is run as two or three families (A/B/C), independent replicate societies with their own random castings (role assignments and lineage-to-seat draws), and the protocols within a family share identical castings, which is what makes the paired contrasts of Section 5 possible. Frozen evaluations redeploy one generation’s notes on fresh castings with learning off. Eliminated seats at finite k see their missed days at their own bandwidth (a paired rerun of one cell under the earlier and later debrief contract finds no difference, Δθ=−0.02 θ=-0.02 [-0.31, +0.29]; supplement). Corpus, audits. The completed corpus holds 7,724 recorded games, 59,589 simulated game-days and 1,905,514 model calls; the analysis set of this paper is 7,416 games and 56,336 simulated game-days: the 6,778-game base battery (4,642 evolution games in 81 chains, 2,136 frozen-deployment games in 49 cells, with 575k statements, 851k ballots and 94k lineage notes) plus the 638 confirmation games of Section 5.4. Integrity is checked end to end: record re-hashing (zero mismatches), a 93.9 GB byte-scan for tooling or identity leakage (zero hits), and per-game contract audits (zero failures; supplement). One defect is disclosed with its exact exposure: in a 15-day window, machine memory pressure occasionally dropped a persisted turn from an agent’s session; 549 games (11.8% of the 4,642 analysis-set chain games; 0.12% of turns) were affected. Excluding them leaves broadcast–silent resolved in 9 of 9 cells; two secondary contrasts lose resolution (supplement table). What a campaign looks like. Figure 3 shows two cells across their sixty generations: one game per family per generation, the hit ratio (mafia lynched ÷ blind-chance expectation) wobbling around a protocol-specific level. Every statics number of the core grid pools exactly this record (all generations and families of a cell, 120–180 games per point), characterizing the whole history, not an endpoint; Section 6 reads the same record in time. Two line plots show, for societies of 26 and 46 players, how often lynches hit mafia members relative to chance in each of 60 generations, as faint per-generation points with bold five-generation averages for broadcast, sequential and silent societies around a dashed chance line. Figure 3. Hit ratio (hits/chance) by protocol at (26,4)(26,4) and (46,5)(46,5): faint points pool the generation’s games across families; bold: centered 5-generation rolling mean. The late undulations are what smoothing does to a persistent, aperiodic series; no periodicity survives the surrogate null (Section 6).Two line plots show, for societies of 26 and 46 players, how often lynches hit mafia members relative to chance in each of 60 generations, as faint per-generation points with bold five-generation averages for broadcast, sequential and silent societies around a dashed chance line. 5. Statics: What the Protocol Does to the Level Where does each society end up, relative to the exact reference? This section carries the paper’s headline numbers; every contrast is paired on matched castings (except (26,4)(26,4) sequential, compared unpaired on its own castings); the cross-size comparison of Section 5.4 is a difference between two such contrasts. 5.1. Communication moves the balance; its form decides for whom On the left, a forest plot gives the estimated lynching tilt with 95 percent intervals for broadcast, sequential and silent societies at nine compositions, every broadcast estimate lying right of the zero-information line, toward the town; on the right, the same estimates at 16 players against mafia density, with an arrow marking up as toward the town and a strip of measured fair lines. Figure 4. (a) Tilt θ θ with 95% game-cluster bootstrap CIs for broadcast, sequential and silent societies at nine (n,m)(n,m) cells, families pooled (120–180 games per point); dashed: the exact reference; right of it favors town. (b) Density scan at n=16n=16 (slopes per unit m/nm/ n: broadcast −0.32-0.32, silence −1.00-1.00); strip: measured fair lines (broadcast 3.73 [3.37, 4.13] vs exact 2.59; silent 2.35; sequential 2.23).On the left, a forest plot gives the estimated lynching tilt with 95 percent intervals for broadcast, sequential and silent societies at nine compositions, every broadcast estimate lying right of the zero-information line, toward the town; on the right, the same estimates at 16 players against mafia density, with an arrow marking up as toward the town and a strip of measured fair lines. Figure 4 is the core comparison; in panel (a), right of the reference line favors the town, left of it the informed minority. Broadcast societies sit toward town of their casting-matched silent societies in 9 of 9 cells, Δθ θ from +0.35+0.35 at (16,2)(16,2) to +1.05+1.05 at (16,4)(16,4); at (46,5)(46,5), +0.62+0.62 [+0.44, +0.81] over 120 paired castings, town rate 0.70 vs. 0.29. Sequential talk, with the same statement budget but speakers hearing earlier statements before committing, recovers far less: it trails broadcast in 7 of 9 cells (+0.35+0.35 to +0.79+0.79; 6 of 9 when memory-affected games or the first ten generations are dropped), exceeds silence in only 3, and sits below silence at (16,2)(16,2) (−0.26-0.26 [-0.48, -0.04]; not resolved once memory-affected games are excluded). Silent societies never rise above the reference and sit below it in 6 cells, the informed minority steering elimination away from itself through the remaining channels, reaching θ^=−0.84 θ=-0.84 (town 0.028) at (16,5)(16,5). Two facts sharpen the reading. First, the broadcast edge pre-dates adaptation: in generation 1, before any notes exist, broadcast−-silent is +1.25+1.25 [+0.54, +2.22] on 23 matched castings — also the only protocol comparison in the corpus with no training-history difference at all (Section 6 identifies its generation-1 carrier and what adaptation does to it). Second, density: silence degrades at −1.00-1.00 [-1.25, -0.77] tilt per unit m/nm/ n, broadcast at −0.32-0.32 [-0.55, -0.10], so the gap grows at +0.69+0.69 per unit; sequential is flat, crossing silence near m=3m=3. In win-probability terms broadcast lifts the measured fair line from the exact 2.59 to 3.73 [3.37, 4.13]; silence and sequential fall below it (Fig. 4b). Excluding the 549 memory-affected games (Section 4) leaves broadcast–silent resolved in 9/9 and changes three secondary contrasts; pooling hides real family structure (per-family tables and the robustness detail in the supplement). 5.2. Bandwidth: response shapes, not yet a law Redeploying one family’s fixed notes across k asks how much of the channel the deployed value needs: where the response crosses the reference it does so at kc≈5k_c≈ 5–77 statements per day at the mid sizes (roughly 1.3m1.3m), but three of six sizes never cross at all, and a parametric saturation fit cannot tell constant, n n, linear-n or ∝m m scalings apart (curves, per-size deployment effects and fits in the supplement). We make no kc(n)k_c(n)-law claim. 5.3. Transfer: family-idiosyncratic, and worse than no notes The 2×22×2 cross-over at (16,3)(16,3) initially suggested a striking rule: family A’s broadcast-trained notes did better silenced, and its silent-trained notes better broadcast (interaction −0.81-0.81 [-1.32, -0.25]). The pre-registered replication with two further note-writing families refutes the rule while confirming the instability: family B shows the same sign without resolving, family C the opposite sign, and the pooled interaction is null (−0.19-0.19 [-0.54, +0.17]; figure in the supplement). What evolved notes do under redeployment depends on the family that wrote them, not systematically on the protocol they grew under. (The matrix’s blank-notes baseline is reported with the dynamics evidence, Section 6.) The same-notes broadcast-vs-sequential contrast resolves only for blank notes (+1.14+1.14 [+0.53, +1.82]): the protocol effect needs no adaptation, and the erasure of Section 5.1 stands as a result about co-adapted societies. Two bounded controls (detail in the supplement): an audience-free private-planning turn did not lift the deployed notes in either family tested (−0.22-0.22, −0.09-0.09; compute not matched); and societies evolved at reduced bandwidth (k=4k=4) land at their silent twins’ level (+0.10+0.10 [-0.20, +0.40]), −0.43-0.43 [-0.73, -0.15] below their full-bandwidth twins — a result Section 5.4 must reckon with. 5.4. Scale: no value of limited talk at (70,6); full broadcast does not fit at 100 A forest plot of lynching tilt for the 70-player arms, their 46-player twins and references, with a cross-size interaction bracket; and an exploratory panel showing the talk-minus-silent deficit concentrated in the early game at 70 players. Figure 5. θ θ at large n: the three matched (70,6)(70,6) arms (40 generations each), the (100,7)(100,7) silent twin, the (46,5)(46,5) full-corpus references, and the like-for-like twin (silent generations 1–20; evolved k=8k=8, k=12k=12); the bracket marks the cross-size interactions; town win counts at right. The exploratory by-phase decomposition is a supplement figure.A forest plot of lynching tilt for the 70-player arms, their 46-player twins and references, with a cross-size interaction bracket; and an exploratory panel showing the talk-minus-silent deficit concentrated in the early game at 70 players. At (70,6)(70,6) — three 40-generation chains with matched castings: silent, k=8k=8, k=12k=12; full bandwidth does not fit (k=8k=8 seats peaked at 188.5k of 192k usable tokens; supplement) — no arm rises above the reference, and talk at k=8k=8 sits resolvably below silence: silent −0.07-0.07 [-0.25, +0.12] (town 16/40), k=8k=8 −0.54-0.54 [-0.81, -0.30] (10/40), k=12k=12 −0.37-0.37 [-0.62, -0.15] (18/40); paired k8−k0=−0.47k8-k0=-0.47 [-0.71, -0.23] (resolved), k12−k0=−0.30k12-k0=-0.30 [-0.64, +0.01] (not; its town count is higher, 18 vs 16). Evolving at reduced bandwidth can fail for other reasons (Section 5.3), so the cell alone confounds scale with limited-bandwidth adaptation. We pre-registered the arbitration: an exact one-size-down twin at (46,5)(46,5), k=8k=8/1212, 20 generations, castings paired to the silent chain. At (46,5)(46,5) both limited-bandwidth arms sit above silence in point estimate (k8−silentk8-silent +0.23+0.23 [-0.16, +0.61], k12−silentk12-silent +0.39+0.39 [-0.14, +0.88], Δ +0.30+0.30 [0.00, +0.60]; full bandwidth on the same castings +0.80+0.80 [+0.30, +1.29]); by the pre-registered rule (either CI above 0 or point estimate >+0.15>+0.15) this selects the size reading, though neither contrast resolves alone. With all 40 (70,6)(70,6) generations the like-for-like cross-size interaction — evolved arms on both sides, matched designs — is resolved at both bandwidths: [k−silent](70,6)−[k−silent](46,5)=−0.70[k-silent]_(70,6)-[k-silent]_(46,5)=-0.70 [-1.15, -0.24] at k=8k=8 and −0.69-0.69 [-1.27, -0.08] at k=12k=12; on matched 20-generation windows it is −0.61-0.61 [-1.19, -0.07] at k=8k=8 and −0.54-0.54 [-1.28, +0.16] at k=12k=12 (unresolved). Under a circular generation-block bootstrap the k=8k=8 interaction and k8−k0k8-k0 hold at every block length, while the k=12k=12 interaction is borderline at block length 5 (supplement). Talk at these bandwidths is worth less at 70 players than at 46. The (46,5)(46,5) silent comparator has 7 of 20 generations in the memory-defect window; dropping them strengthens both interactions (−0.85-0.85, −0.93-0.93), a conservative exposure. One measured misfit is reported with it: at (70,6)(70,6) the scalar tilt under-predicts the talking arms’ town wins (observed minus tilt-predicted town rate +0.23+0.23 [+0.15, +0.30] at k=12k=12, +0.11+0.11 [+0.02, +0.18] at k=8k=8, −0.01-0.01 silent; Fig. 1 marks every such gap, including the (46,5)(46,5) sequential arm’s +0.12+0.12). Two exploratory readings address this and the long-transcript objection: the talking arms’ deficit is front-loaded (days 1–10: −0.75-0.75 at k=8k=8, −1.27-1.27 at k=12k=12; day 21 on: −0.30-0.30 [-0.67, +0.04] and +0.13+0.13 [-0.32, +0.59]; supplement figure), when transcripts are short; on day-matched windows (days 11–20) the interaction is resolved at both bandwidths (−1.11-1.11, −1.36-1.36); and a bulk/endgame refit resolves the k=12k=12 misfit (θend−θbulk=+1.33 _end- _bulk=+1.33; predicted town 0.50 vs observed 0.45) but not k=8k=8. Comparability: each arm is one family; the (46,5)(46,5) silent comparator predates its k-arms (served texts byte-equal under masking), while the (70,6)(70,6) trio ran concurrently. The (100,7)(100,7) silent twin plays at the reference (+0.11+0.11 [-0.16, +0.39]), declining late (−0.89-0.89 [-1.59, -0.30]); two single finite-k generations are descriptive only. Full-bandwidth talk at n=100n=100, however, is not merely expensive; it does not fit this architecture: a measured k=20k=20 game overflowed a surviving seat’s 200k-token context by day 38, and at the measured per-day token costs a full-bandwidth survivor would need ∼ 330k (measurement, proactive stop and projection separated in the supplement). The bound is a property of this model, memory and protocol stack (summarization, output caps or longer contexts would move it), but within the stack it is a hard trade: open discussion’s context cost grows with lifetime × bandwidth (cf. the scale–expressiveness trade-off of LLM ABMs (Chopra et al., 2025)), and the measured value at the bandwidths that fit had already vanished. A detective variant at (26,4)(26,4), in which one citizen privately learns one true role per night, did not resolvably raise the town’s win rate (0.650 [0.56, 0.73] vs. 0.608 for matched twins; tilt lift +0.16+0.16 [-0.12, +0.45], family A +0.63+0.63, family B −0.32-0.32) and stays below an exact benchmark that adds a trusted detective to the twins’ measured edge (0.770; binomial p=0.003p=0.003; conventions in the supplement). Section 7 shows one reason disclosure is costly. The bandwidth, detective, density, cross-over and scale tests were pre-registered: hypotheses and decision rules fixed before the data, and the supplement lists each with its outcome, including the failed and refuted predictions. The dynamics and behavior analyses of Sections 6–7 are exploratory analyses of the locked records. On the left, line plots over 60 generations show the share of day-1 statements in which broadcast citizens, broadcast mafia and sequential citizens say they are citizens, with the day-1 rate of lynching mafia relative to chance below, both dropping sharply after the first generation; on the right, for frozen 16-player games on the same 40 castings, bars and strips compare blank notes with six evolved note sets on claim rate, day-1 accuracy and overall tilt, blank notes giving the highest claim rate and tilt. Figure 6. The tell and its self-destruction. (a) First-day role-claim rates in broadcast societies by generation (window means bold; sequential citizens dashed; log axis), with the first-day mafia-hit factor per window below: the 3×3× edge decays as citizens stop claiming; mafia claims never return. (b) Frozen redeployment on 40 identical castings at (16,3)(16,3): every generation-60 note set suppresses the claims; family C’s broadcast-trained notes install a substitute cue (hits 3.73×3.73×). Bottom strip: θ θ at full deployment; evolved −- blank resolved for five of six families.On the left, line plots over 60 generations show the share of day-1 statements in which broadcast citizens, broadcast mafia and sequential citizens say they are citizens, with the day-1 rate of lynching mafia relative to chance below, both dropping sharply after the first generation; on the right, for frozen 16-player games on the same 40 castings, bars and strips compare blank notes with six evolved note sets on claim rate, day-1 accuracy and overall tilt, blank notes giving the highest claim rate and tilt. Two forest plots on logarithmic axes: how often the day's first speaker is lynched relative to a position-blind expectation under sequential play and in a broadcast placebo, overall and by role; and the night-kill risk ratio of citizens whose ballot targeted a mafia member, for every arm. Figure 7. (a) First-speaker lynch rate over the position-blind rate: sequential 1.66 [1.58, 1.73] vs. the broadcast placebo (the engine’s own order draw) 1.00; within role, citizens 1.72, mafia 1.25. (b) Ballot-accuser night-kill risk ratio — citizens whose ballot went to a mafia member that day — one point per arm (log scale, reference 1): 1.10–3.26, CI above 1 in 30 of 31 arms, highest under silence in 9 of 9 cells. Associations in the recorded games; no causal claim.Two forest plots on logarithmic axes: how often the day's first speaker is lynched relative to a position-blind expectation under sequential play and in a broadcast placebo, overall and by role; and the night-kill risk ratio of citizens whose ballot targeted a mafia member, for every arm. 6. Dynamics: From the Prior to the Adapted Society How do societies travel from the model’s untrained prior to adapted play? Claim statistics use extractors validated blind (supplement on validation provenance); time-series tests use permutation or AR(1)-surrogate nulls with Benjamini–Hochberg correction within each family of tests. The prior and its tell. Untrained societies arrive with an honest convention. In the first games of the 23 casting-matched broadcast chains, citizens open with an explicit “I am a citizen” (91% of 351 statements) and mafia mostly do not (30%), so a missing claim is evidence: the first day’s lynch hits mafia in 13 of 23 games against 4.3 expected (3.0×3.0×, p=4×10−5p=4×10^-5). The lynched mafia are almost all non-claimers (the missing claim is one cue among several: ∼ 40% of the faction effect in a conditional-logit decomposition). The edge is a property of the untrained model’s prior and of the protocol that exposes it. In the same chains’ silent first games the day-1 lynch is at the zero-information rate (7/25 vs 4.5, p=0.18p=0.18); under turn-taking it points below chance (1/23 vs 4.3, p=0.10p=0.10): mafia who speak after claimers copy the claim (2% having heard none, 39% after three), and the day’s first speaker, usually a citizen, draws the lynch (Section 7). The 40 blank-notes redeployments replicate all three patterns on fresh castings (broadcast 95%/19%, 3.2×3.2×; silent p=1.0p=1.0; sequential 4/40 vs 7.5). The collapse. Societies un-learn the convention from the citizens’ side, fast: broadcast citizen claims fall 91%→21%91\%→ 21\% by generations 2–3 and settle at 13%, while mafia claims drop to ≤ 0.6% and never recover — the convention collapses at generation 2 in 21 of 23 broadcast chains, and first-day accuracy decays in step (3.0×→1.7×→1.2×3.0×→ 1.7×→ 1.2× chance). A late claim remains almost a certificate (mafia are 4 of 935 late claimers), but with 87% of citizens silent about their role, non-claiming carries almost no information (lift 3.53→1.123.53→ 1.12): the citizens’ own change of convention removes the most informative first-day cue. The notes carry the change, but not as doctrine. Frozen cross-deployment isolates the cause and prices it. On 40 identical castings at (16,3)(16,3), blank-notes societies reproduce the untrained pattern (95% claims, first-day hits 3.2×3.2×) and score θ^=+1.36 θ=+1.36 [+0.90, +1.90] (town 31/40), while every generation-60 note set, silence-evolved included, suppresses the claims (2–24%); five of six also remove the first-day edge (hits ≤1.2×≤ 1.2×; the sixth, family C’s broadcast notes, installs a “framework” cue, 3.73×3.73×), and every family scores below blank (evolved −- blank −1.37-1.37 [-1.97, -0.83] for broadcast-trained, −1.25-1.25 [-1.85, -0.73] for silence-trained; resolved for five of six; family C −0.51-0.51 [-1.24, +0.13]), with the broadcast-over-silent deployment gap larger without notes (+1.14+1.14). Together with the generation-1 result this locates the broadcast advantage in the pretrained model: sixty generations of self-authored notes, at this size and in redeployment, cost more than they add, and not only on day 1 (days 2 and later: −1.37-1.37 [-2.02, -0.79], −1.02-1.02 [-1.68, -0.45]). Yet the insight is written early in only 9 of 56 chains (median first writing: generation 19), and generation-2 citizens whose notes say nothing about claims still fall to 18.8%. Every inherited note set we observed extinguished the naive convention, whether or not it mentioned claims (a generic format effect is not ruled out; notes that advise claiming push the other way, 79% claiming). The regime: no cycles; broadcast gives memory. Across 75 chain and 30 cell series, no periodicity survives the AR(1)-surrogate null and correction: the wave-like late curves of Fig. 3 are what smoothing does to a persistent, aperiodic series. What is systematic is protocol-specific, statistic by statistic. Broadcast hit ratios carry lag-1 memory (ACF +0.14+0.14, p=0.001p=0.001; +0.17+0.17 over silent, +0.13+0.13 over sequential; robust to dropping the first ten generations and to excluding the memory-affected games, but not replicated in the six broadcast chains the defect never touched, which are also the smallest cells — exposure and size are confounded; supplement). All three protocols fluctuate beyond a constant-edge noise floor, broadcast resolvably more than silence (+0.28+0.28 log-variance). Casting-matched families drift apart beyond a shared constant edge under broadcast in generations 21–40 (p=4.8×10−4p=4.8×10^-4; over the full span the protocol contrasts are borderline). Underneath, outcomes show no detected change of level (last third vs middle third: 0 of 30 cells; early-vs-late tilt: 3 of 34 arms, both directions, ≈ 1.7 expected by chance). The notes show no sign of converging in wording (≈ 0.89 rewritten every generation, no downward trend; vocabulary overlap rises, so this is surface change, not necessarily policy change; they double in length under talk, 420→ 897 words). One adapted outcome is a deterioration: the (16,5)(16,5) broadcast collapse develops in the first generations (generations 1–5: town 9 of 15, θ θ +1.17+1.17 [+0.34, +2.02]; all generations: 26%), as pre-registered; mafia-role experience per lineage is five times higher at m=5m=5 than at m=1m=1, a confound this design cannot separate. Over sixty generations the notes keep changing while outcomes show no systematic trend; what broadcast talk changes is the coupling: generations cohere, families individuate. 7. Behavior: Inside the Games What do half a million statements and 851k ballots show the societies doing? Extractors are hand-validated blind (precision 50/50 on claims; meme counts are lower bounds); everything here is an association in the recorded games. Mafia rarely claim, and claimers fare worse. Broadcast mafia claim to be citizens in 60 of 27,972 statements (0.21%, vs. 2.77% for citizens); the few who do are lynched more, not less, the same day (O/E 1.79 [1.01, 2.68]). Under turn-taking mafia claim at 0.46×0.46× the citizen rate, and the claims are overwhelmingly copies rather than initiatives: claim probability jumps from 0.005 to 0.41 (citizens) and 0.0003 to 0.24 (mafia) after an earlier claim, and 220 of 221 later-position day-1 mafia lies follow one, consistent with documented LLM conformity (Zhu et al., 2025). Honest signals are costly too: broadcast citizens who claim draw the night kill at O/E 1.37 [1.21, 1.56], and the detective that announces itself is killed the following night 40 of 46 times (O/E 12.6) — while no mafioso ever counterfeited a detective claim in 120 detective games, and confession is an endgame concession (87% on the final day). Turn-taking herds speech, not ballots. Sequential statements cascade in the sense of (Bikhchandani et al., 1992) (above), and the cascade carries coordination without information: landslide days (≥ 75% of ballots on one seat) are as frequent as in broadcast (13.8% vs. 13.3%) but land on mafia near chance (1.08×1.08× vs. 2.53×2.53× for broadcast); the bandwagon index — the probability that a ballot follows the day’s most-accused seat — is indistinguishable (0.48 vs. 0.47, ≈ 5× chance). When a sequential day opens with an accusation, later statements name the target more than in broadcast, yet ballots follow less (0.84 vs 0.62; 0.34 vs 0.43; lynched 0.38 vs 0.53). What turn-taking anchors on is the first speaker: named in 49% of later statements (broadcast 18%), lynched at 1.66×1.66× [1.58, 1.73] the position-blind rate (broadcast placebo 1.00×1.00×), mostly a citizen; first and last speakers are also night-killed more often (1.33×1.33×, 1.41×1.41×). Under turn-taking the channel carries exposure and imitation; under broadcast, where statements are composed independently, landslides are accurate, consistent with human evidence that exposure to others’ judgments erodes crowd accuracy (Lorenz et al., 2011). Night kills fall on the citizens who found the mafia. Citizens whose ballot went to a mafia member that day are night-killed at risk ratios 1.10–3.26 (30 of 31 arms), most under silence (9 of 9 cells), where no statements compete with the ballot record. Ballot accuracy tracks the protocol ordering of Section 5.1: citizens’ ballots land on mafia above chance in broadcast (9/9 cells), near chance in silence, and below chance in sequential play (resolved in 4 of 9 cells). Mafia discipline completes the picture: partner ballots far below chance (0.61% vs 16.1% at k=0k=0), accusations at 0.30×0.30× the citizen rate. The written culture. The notes concentrate on observables: vote-pattern tracking appears in 88.9% of all 94k notes, and “analysts get killed” — the lesson of the night hazard above — rises from 27.8% to 73.3% of broadcast notes across the chains while peaking at 8.6% in silent ones: the societies write down the dangers they can see. Take-away. Claimants, accurate voters and the self-announced detective all draw the night kill more often, consistent with the night removing the honest signals of Section 6. Turn-taking keeps coordination but not information: its landslides account for about two-fifths of its accuracy deficit, the rest coming from ordinary days (0.82×0.82× vs 1.06×1.06×). These are associations, not tested mediators of Section 5’s contrasts. 8. Related Work Mafia’s theory: Braverman, Etesami and Mossel (Braverman et al., 2008) prove the Θ(R) ( R) fair line (with R the population) for town play implemented by simultaneously announced random numbers (in turn, they could be steered); our protocols vary the same commit-before-observing structure for language (Knight, 2026); (Yao, 2008) gives recursion-based bounds and argues BEM’s multi-round conjecture conditionally (its information-zero exponent proved under weak-majority stopping by (Tamashiro, 2026), a partly machine-checked working paper); (Migdał, 2010) gives the exact zero-information solution we use, and (Stock and da Silva, 2026) studies suspicion dynamics. The nearest analytic treatment of LLM Mafia play fits a capability model to a four-player, single-day variant (Costa and Vicente, 2026); we anchor multi-day societies of 8–100 to Mafia’s own exact theory, with protocol, bandwidth and density as manipulanda. LLM social deduction more broadly optimizes agents (Xu et al., 2024; Xu et al., 2025; Jin et al., 2024), improves frozen agents through stored reflections (Xu et al., 2023), evaluates at scale in fixed small games (Doerschuk-Tiberi et al., 2026; Bailis et al., 2024), times speech in asynchronous chat (Eckhaus et al., 2025), and compares discussion against none (O’Gara, 2023); in cooperative evaluation, one-by-one, simultaneous and summarized exchange peak at similar accuracy (Chan et al., 2024); in our competitive setting the format decides most of the value. Learning-to-communicate work trains the channel, mostly cooperatively (Foerster et al., 2016; Lowe et al., 2019), reaching competition recently (Noukhovitch et al., 2021); in RL Werewolf a learned signal helps one faction non-linearly (Brandizzi et al., 2021). Our contribution is not corpus size but design: matched-casting protocol interventions across sizes, measured against an exact reference, with an adaptation record long enough to test dynamics against surrogate nulls. 9. Discussion and Limitations Reading. The value of communication here is a property of the protocol: simultaneous composition keeps the channel informative; under turn-taking it carries imitation and exposure; under silence the minority’s ballots and night choices dominate. What adaptation adds is protocol-specific, transfers unstably, and shows no systematic improvement: its fastest, most uniform act removes the most informative first-day cue, written culture trailing it; regime-wise, no detected trend under continual rewriting, family individuation only under broadcast. For multi-agent LLM design: more communication is not always better (far less when speakers react first), and accumulated self-generated experience can subtract value while appearing to encode lessons (Xiong et al., 2026). Limitations. One model at pinned settings (one injection probe); the generation-1 convention and its collapse are properties of this model’s prior and prompt stack (no transfer claim); self-written notes are one adaptation path. Frozen bandwidth curves use one family per size amid large heterogeneity; the pre-registered matrix added two families and refuted the single-family cross-over rule (§5.3). Each (70,6)(70,6) arm is one family; the (46,5)(46,5) silent comparator is non-concurrent; the scalar tilt under-predicts the talking arms’ wins there (§5.4). Dynamics tests use one game per generation per chain (strong periodicity excluded, not every cycle); behavior results are associations under selection, extractor recall bounded and disclosed. The planned interventions on nights, ballots and history were not run. The nine headline contrasts survive Holm and BH (Bonferroni marginal at (8,2)(8,2)); broadcast−-silent is positive in 23 of 23 families, resolved in 18 (supplement). 10. Conclusion Against Mafia’s exact zero-information reference, these LLM societies profit from statements composed independently and simultaneously; reaction-first discussion carries imitation and exposure instead; silence favors the informed minority; and limited talk is worth less at 70 players than at 46, below silence at k=8k=8. 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