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.
Figures & tables
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=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.
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) , 40 at (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.
Figure 3. Hit ratio (hits/chance) by protocol at (26,4) and (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.
Figure 4. (a) Tilt θ^ with 95% game-cluster bootstrap CIs for broadcast, sequential and silent societies at nine (n,m) cells, families pooled (120–180 games per point); dashed: the exact reference; right of it favors town. (b) Density scan at n=16 (slopes per unit m/n : broadcast −0.32 , silence −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 5. θ^ at large n : the three matched (70,6) arms (40 generations each), the (100,7) silent twin, the (46,5) full-corpus references, and the like-for-like twin (silent generations 1–20; evolved k=8 , k=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.
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× edge decays as citizens stop claiming; mafia claims never return. (b) Frozen redeployment on 40 identical castings at (16,3) : every generation-60 note set suppresses the claims; family C’s broadcast-trained notes install a substitute cue (hits 3.73× ). Bottom strip: 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.
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.
We study group decision-making in artificial societies where the rules of play are themselves subject to collective amendment. Using the self-amending game Nomic, we compare multiple scales across two LLM families and find that collective adaptation does not improve monotonically with model size. Instead, both families exhibit a narrow mid-scale regime that supports sustained rule adoption, diverse amendments, and balanced consensus. Smaller models tend to remain rule-inert, whereas larger models often converge on restrictive voting patterns, and heterogeneous mixed-size groups collapse into veto-driven gridlock. These cross-scale contrasts persist under temperature perturbations and under a shift from unanimity to majority voting, although latent-state structure varies by family and scale. Hidden-state divergence alone does not explain collective performance: high representational divergence can coincide with poor behavioural outcomes. Linear probes reveal regime-selective coupling between latent vote-predictive signals and collective behaviour, but decodability is necessary rather than sufficient for adaptive play. Overall, the recurring regularity is non-monotonicity, not the particular scale at which the optimum appears. Self-amending games therefore provide a controlled testbed for studying collective adaptation in artificial societies beyond raw model scale.
Kazuya Horibe, Masaomi Hatakeyama, Gen Masumoto +2
Center for Brain Science, RIKEN. · Department of Evolutionary Biology and Environmental Studies, University of Zurich. · Information R&D and Strategy Headquarters. +3
An LLM agent's public behaviour reveals little about its social reasoning: an agent that votes correctly may be guessing, and an agent that lies well leaves no trace of what it actually believes. We present MafiaScope, an open testbed that turns the social deduction game Mafia into a measurement instrument for machine Theory of Mind. After every public utterance, every agent privately answers a configurable set of structured probe questions; the answers never re-enter the game and are scored automatically against the ground truth the engine knows. An interactive visualizer renders the belief trajectories: impersonate mode shows the game as one agent sees it, panels chart timeline-aligned accuracy and calibration, and counterfactual replay forks any recorded step. In a 32-game DeepSeek case study with 13{,}815 parsed probe answers, stated confidence is poorly calibrated, with expected calibration error 0.17, agents over-predict being suspected 1.5 times, and a 30-fork replay experiment walks the counterfactual replay workflow end to end. Engine, viewer and a corpus of 200+ cross-model games are released under an open licence; live demo: https://karpovilia.github.io/mafiascope/; screencast: https://vimeo.com/1208920221.
In security-sensitive applications, language-model agents are often required to coordinate without disclosing confidential information. Yet repeated interactions may also let ordinary messages acquire shared private meaning. We study a repeated game with pairs of models in which the sender model observes one of four secret states and selects one of four summaries of the same public report, while the receiver model tries to infer the secret state. We find that model pairs can learn to communicate the secret using only one bit of feedback indicating whether the receiver inferred it correctly. This learning occurs during inference with fixed parameters and no supplied codebook or encoding examples. The effect also persists when agents generate their own free-form updates in a simulated incident-response task. Across ten independent games, pairs of GPT-5.6 Sol agents reach 98.8% final accuracy, compared with 25% chance, despite explicit instructions prohibiting disclosure and a monitor that screens each message without access to the agents' interaction histories. The same interactions that help agents cooperate can therefore allow confidential information to pass through messages intended for legitimate coordination.
Jacob Dineen, Silei Ren, Muhao Chen +2
Arizona State University · Cornell University · University of California, Davis +1