Triadic Werewolf: A Jester Role for Multi-Hop Theory of Mind in LLMs

Technical Summary: Triadic Werewolf: A Jester Role for Multi-Hop Theory of Mind in LLMs

Problem Statement
Current benchmarks for evaluating Theory of Mind (ToM) in Large Language Models (LLMs) within social-deduction games (e.g., Werewolf, Avalon) are predominantly dyadic. These games split players into two opposing factions (e.g., Villagers vs. Werewolves), creating a scenario where every observable cue points to a single hidden side. Consequently, a model can achieve high scores by exploiting surface-level heuristics (e.g., "hesitation implies Werewolf") without genuinely simulating opponents' incentives or reasoning about hidden mental states. This is termed the cue-sufficiency problem: a high score under dyadic conditions does not necessarily indicate genuine multi-hop ToM reasoning, as the optimal policy and a pure cue-reading policy often select the same action.

Methodology
To break this coincidence, the authors introduce Triadic Werewolf, a 10-player benchmark that adds a third faction: the Jester.

• Game Architecture: The game includes 6 Villagers, 2 Werewolves, 1 Doctor, and 1 Jester. The Jester's utility function is inverted: it wins if and only if it is voted out (exiled) by the majority during the day. Conversely, Werewolves win by eliminating Villagers, and Villagers win by eliminating Werewolves.
• The Incentive Conflict: This structure creates cue ambiguity. A player exhibiting high suspicion is ambiguous evidence: they could be a Werewolf (whom Villagers should exile) or a Jester (whom Villagers should not exile, as exiling them causes a Villager loss). Werewolves must also reason that exiling a high-suspicion player might be a Jester, which would end the game in a Werewolf loss.
• Experimental Design: The study evaluates three frontier models (GPT-4.1, DeepSeek-V3.1, Llama-3.3-70B) across 60 games (10 games per model per condition).
  • Conditions: A Jester self-learning loop is toggled ON/OFF. In the ON condition, the Jester model summarizes the game, extracts lessons (tactics, to-dos, to-avoids), and appends them to a persistent learning file fed back into the system prompt for subsequent games.
  • Metrics: Outcomes are measured by faction win rates, voting dynamics (specifically Day 1 votes), and behavioral analysis of deception types and suspicion scores.
  • Control: A dyadic control (removing the Jester and adding a sixth Villager) is run on GPT-4.1 to isolate the effect of the triadic structure.

Key Contributions

1. Triadic Benchmark: A 10-player Werewolf variant where the Jester's inverted utility breaks the cue-sufficiency of standard dyadic deduction games, forcing agents to reason across three competing utility functions.
2. Controlled Evaluation: A systematic evaluation of self-learning loops in a deceptive context, measuring first-order gains for the Jester and second-order effects on other factions.
3. Mechanistic Analysis: A deductive coding of 141 accumulated Jester lessons, categorizing them by strategy and Theory of Mind order (1st-order: bare imperative; 2nd-order: referencing others' perceptions; 3rd-order: explicit contrast across two faction perceptions, e.g., "appear wolf-like without appearing villager-aligned").

Results

• Jester Dominance: Across all models, the Jester wins 55–70% of games, while Werewolves rarely exceed 20%. This suggests models fail to resolve the cue ambiguity, often treating high-suspicion players as Werewolves to be exiled, inadvertently helping the Jester.
• Self-Sabotage: Werewolves frequently vote for the Jester on Day 1 (60–70% for GPT-4.1), a strictly self-defeating action that ends the game in a loss for the Wolf faction. This indicates a failure to model the Jester as a distinct third party with different incentives.
• Substitution Effect: When the self-learning loop improves the Jester's win rate, the loss is absorbed almost entirely by the Villagers, not the Werewolves. Werewolves were already failing the inference task; the Jester's gains come from exploiting Villager belief-updating.
• Model-Specific Learning:
  • DeepSeek-V3.1: Shows the largest gain from self-learning (+40% win rate). It is the only model that reliably produces 3rd-order ToM entries (15.4% of lessons), explicitly learning to mimic a Wolf while avoiding Villager alignment.
  • GPT-4.1: Shows a ceiling effect; it starts with a high Jester win rate (70%) and self-learning provides little improvement or even slight degradation in some metrics. It relies on erratic behavior and aggression rather than nuanced contrastive reasoning.
  • Llama-3.3-70B: Shows moderate gains (+20%) but relies on 1st and 2nd-order reasoning (bare imperatives or simple perception references) without the explicit triadic contrast.
• Deception as a Model Property: Deception styles (e.g., fabrication vs. distortion) are consistent across roles for a given model, suggesting models apply a fixed "deception aesthetic" rather than adapting strategies based on opponent incentives.

Significance and Claims
The paper claims that triadic incentive structures expose a layer of multi-agent reasoning that dyadic games leave invisible. The results indicate that current frontier LLMs do not reliably perform the multi-hop ToM inference required to distinguish between a "suspicious Villager/Jester" and a "suspicious Werewolf" when the correct action depends on the hidden role's utility.

The study argues that high scores in dyadic benchmarks may be artifacts of cue-sufficiency rather than genuine mental-state reasoning. The failure of models to prevent the Jester's victory—specifically the Werewolves' self-sabotage and the Villagers' inability to distinguish the Jester from a Wolf—serves as a behavioral signature of this limitation. Furthermore, the paper demonstrates that self-learning loops can help models acquire complex, contrastive strategies (as seen in DeepSeek-V3.1) but can also degrade performance in models that have already saturated the task or rely on different heuristics (as seen in GPT-4.1).

The authors conclude that the Jester win-rate serves as a direct measure of multi-hop ToM failure and that the triadic setup is a necessary structural change to evaluate whether LLMs can truly reason about competing incentives beyond surface-level pattern matching.