The Stackelberg Speaker: Optimizing Persuasive Communication in Social Deduction Games
Pith reviewed 2026-05-18 08:20 UTC · model grok-4.3
The pith
Modeling turn-based dialogue in social deduction games as a Stackelberg leader-follower game allows reinforcement learning to train agents that optimize utterances for greater persuasive effect.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Turn-based dialogue in social deduction games is formalized as a Stackelberg competition in which the speaker acts as leader and chooses utterances to influence follower responses; a reinforcement learning framework optimizes these utterances for persuasive impact and produces agents that outperform baselines across three different games.
What carries the argument
The Stackelberg leader-follower formalization of dialogue, in which the leader's utterance choice is optimized to shape the follower's subsequent belief and action, which supplies the training signal for the reinforcement learning objective.
If this is right
- Agents learn to generate speech that reliably steers other players toward desired alignments rather than depending on fixed dialogue templates.
- Performance improvements arise specifically from treating communication as an optimizable influence action instead of a byproduct of deduction.
- The same leader-follower structure can be applied to any turn-based interaction where one participant seeks to shape another's next move.
- Training focuses on the downstream effect of an utterance on the follower's policy rather than on surface-level fluency or information content alone.
Where Pith is reading between the lines
- The method may transfer to non-game settings such as negotiations or team coordination where one party needs to persuade others without direct commands.
- Human opponents facing these agents could develop new defensive strategies, altering the equilibrium of the game over repeated play.
- Extending the model to simultaneous or multi-leader settings would test whether the core persuasion advantage persists when multiple speakers compete for influence at once.
Load-bearing premise
That representing one player's utterance as a leader move and the others as follower responses accurately describes how beliefs are updated and actions are chosen in response to persuasion.
What would settle it
An experiment in which agents trained under the Stackelberg reinforcement learning objective show no performance gain over baselines in a social deduction game variant where persuasion has no measurable effect on other players' responses or final outcomes.
read the original abstract
Large language model (LLM) agents have shown remarkable progress in social deduction games (SDGs). However, existing approaches primarily focus on information processing and strategy selection, overlooking the significance of persuasive communication in influencing other players' beliefs and responses. In SDGs, success depends not only on making correct deductions but on convincing others to response in alignment with one's intent. To address this limitation, we formalize turn-based dialogue in SDGs as a Stackelberg competition, where the current player acts as the leader who strategically influences the follower's response. Building on this theoretical foundation, we propose a reinforcement learning framework that trains agents to optimize utterances for persuasive impact. Through comprehensive experiments across three diverse SDGs, we demonstrate that our agents significantly outperform baselines. This work represents a significant step toward developing AI agents capable of strategic social influence, with implications extending to scenarios requiring persuasive communication. Our code and data are available at https://3dagentworld.github.io/leader_follower.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims to formalize turn-based dialogue in social deduction games (SDGs) as a Stackelberg competition, with the current player as the leader strategically influencing the follower's response. It proposes a reinforcement learning framework to train agents to optimize utterances for persuasive impact and reports that these agents significantly outperform baselines across three diverse SDGs.
Significance. If the experimental results hold under rigorous controls, this could represent a meaningful advance in developing LLM agents capable of strategic social influence beyond mere information processing. The work highlights the importance of persuasive communication in SDGs and provides a game-theoretic lens for it. However, the absence of detailed baselines and evaluation protocols in the abstract raises concerns about the robustness of the claimed gains.
major comments (2)
- Experimental Results section: the abstract reports outperformance over baselines but provides no details on the specific baselines used, evaluation metrics, statistical tests applied, or controls for confounding factors such as prompt engineering variations. This omission prevents assessment of whether the performance gains are attributable to the Stackelberg formulation rather than standard LLM prompting.
- Modeling section (Stackelberg formalization): the leader-follower structure assumes the follower selects a best response to the committed utterance through an accurate belief-update function. The described RL setup uses the same LLM for leader and follower roles without an explicit belief tracker or Bayesian update step, which risks reducing the claimed strategic influence to ordinary next-token prediction on dialogue history.
minor comments (2)
- The availability statement for code and data at https://3dagentworld.github.io/leader_follower should be repeated in the main body or appendix for reader convenience.
- Abstract: consider briefly naming the three SDGs and the type of baselines (e.g., standard LLM agents or non-Stackelberg RL) to give immediate context to the outperformance claim.
Simulated Author's Rebuttal
We thank the referee for their constructive feedback, which highlights important aspects of clarity and rigor in our presentation. We address each major comment below and indicate the planned revisions.
read point-by-point responses
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Referee: Experimental Results section: the abstract reports outperformance over baselines but provides no details on the specific baselines used, evaluation metrics, statistical tests applied, or controls for confounding factors such as prompt engineering variations. This omission prevents assessment of whether the performance gains are attributable to the Stackelberg formulation rather than standard LLM prompting.
Authors: We agree that additional detail strengthens the evaluation. The Experimental Results section already specifies the baselines (vanilla LLM prompting without RL, non-Stackelberg RL agents, and heuristic persuaders), metrics (persuasion success rate and overall game win rate), and reports statistical significance via paired t-tests. To further isolate the contribution of the Stackelberg formulation, we will add an ablation study that systematically varies prompt templates and reports the resulting performance differences in the revised manuscript. revision: yes
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Referee: Modeling section (Stackelberg formalization): the leader-follower structure assumes the follower selects a best response to the committed utterance through an accurate belief-update function. The described RL setup uses the same LLM for leader and follower roles without an explicit belief tracker or Bayesian update step, which risks reducing the claimed strategic influence to ordinary next-token prediction on dialogue history.
Authors: We appreciate this distinction. The theoretical model indeed assumes an idealized best-response follower with belief updates. In the implemented RL framework, the shared LLM generates follower responses conditioned on the full dialogue history, which serves as an implicit representation of updated beliefs through the model's contextual reasoning. This design choice enables end-to-end optimization of persuasive utterances via RL without requiring a separate belief module. We will revise the Modeling section to explicitly acknowledge this approximation, discuss its relationship to the Stackelberg formalization, and note the limitation relative to explicit Bayesian tracking. revision: partial
Circularity Check
No circularity: derivation uses external game theory and RL without self-referential reduction
full rationale
The paper's core chain formalizes SDG dialogue as a Stackelberg leader-follower game and applies standard RL to optimize leader utterances for persuasive impact, then validates via experiments on three games. No quoted equations, fitted parameters, or self-citations reduce the claimed performance gains to quantities defined by construction within the paper itself. The Stackelberg structure and RL framework draw on established external methods; the outperformance is presented as an empirical result against baselines rather than a tautological renaming or prediction forced by internal fits. This is the most common honest non-finding for papers that import standard formalisms without making the central claim depend on self-defined quantities.
Axiom & Free-Parameter Ledger
free parameters (1)
- RL training hyperparameters
axioms (1)
- domain assumption Listener responses can be modeled as rational reactions to the speaker's utterance in a Stackelberg game structure
Lean theorems connected to this paper
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We formalize turn-based dialogue in SDGs as a Stackelberg competition... propose a reinforcement learning framework that trains agents to optimize utterances for persuasive impact... GRPO
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
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- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
discussion (0)
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