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Cheap Talk Stabilizes Strategic Interaction in LLM Agents

Nunzio Lorè, Hongan Zhu, Babak Heydari

arXiv:2609.16270v1cs.MA

TL;DR

Repeated interaction makes individual action persistence relevant because one agent’s action enters another’s later context, yet whether cheap talk stabilizes LLM policies and how is unclear. The paper tests non-binding pre-play messages across repeated games and uses counterfactual and activation interventions to examine mechanisms; switching falls overall, with effects varying by model and history.

  • Problem

    Repeated interaction makes action persistence relevant because one agent’s action enters another’s later context, yet whether cheap talk stabilizes LLM policies and through which mechanisms is unclear.

    Source: §1 · p. 1

  • Method

    The study tests non-binding pre-play messages across four repeated games and six contexts, then uses message/history counterfactuals and closed-loop activation interventions to probe mechanisms.

    Source: §1 · p. 1, §6 · p. 7

  • Results

    Across four repeated games, switching fell from 63.8% to 18.9%, with 71 of 96 cell-level effects stabilizing after correction and five reversals in social or team framings.

    Source: §6 · p. 7

  • Takeaways & Limitations

    Cheap talk can make individual trajectories more persistent rather than merely shift average behavior, while its mechanisms depend on message content and recent partner behavior.

    Source: §1 · p. 1, §6 · p. 7

    The evidence covers four open-weight 7–9B checkpoints and ten-round interactions; activation interventions are limited to Qwen and Falcon in Prisoner’s Dilemma, leaving broader generalization open.

    Source: §6 · p. 7

Abstract

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Large language models are increasingly deployed as interacting agents, making the persistence of their action policies across repeated interaction critical for reliable multi-agent operation. We investigate whether and how agent-generated, non-binding pre-play communication ("cheap talk") increases such persistence in four open-weight 7-9B-parameter LLMs. Our experiments span four repeated two-player games -- Prisoner's Dilemma, Snowdrift, Stag Hunt, and Harmony -- with incentive structures ranging from strategic conflict to alignment, each presented in six contexts. We observe unstable trajectories in all four games, although their prevalence and magnitude depend strongly on model and context. Across models, games, and contexts, cheap talk is predominantly stabilizing, with five corrected reversals concentrated in social or team framings; effects vary substantially by model and context. Controlled current-message interventions identify two separable output-level channels in Qwen: reduced action uncertainty and less between-round drift in action probabilities. Matched history-by-message counterfactuals further show that recent partner behavior conditions how mutual-benefit versus self-prioritizing language affects policy persistence. Finally, in Prisoner's Dilemma, we identify in Qwen and Falcon a history-balanced policy-content direction in late transformer layers; projecting out this direction increases realized switching during closed-loop play, demonstrating that complete trajectories are causally sensitive to this component. Together, these findings show that cheap talk can make individual trajectories more persistent across diverse incentive structures, while revealing that the magnitude and mechanisms of stabilization are model- and history-dependent.

1 Introduction

The paper asks whether non-binding pre-play communication stabilizes individual LLM policies in repeated games, where actions feed into partners’ later contexts. Across diverse games and framings, cheap talk usually reduces switching, with follow-ups separating output-level from representation-level mechanisms.

1 Introduction

  • Because one agent’s action enters another’s later context, small behavioral fluctuations can compound across rounds, making predictability relevant to reliable multi-agent operation.The paper measures first-order action persistence rather than treating every action change as irrational or as a complete measure of predictability.Source: §1 · p. 1
  • Cheap talk is costless and non-binding, so it can change expressed intentions without changing incentives; its effects may also depend on recent play.The paper asks whether it stabilizes repeated interaction and through which mechanisms.Source: §1 · p. 1
  • The evaluation covers four open-weight 7–9B models, four repeated games, six framings, and communication versus no-communication treatments.The study uses 19,200 ten-round dyads.Source: §1 · p. 1
  • Across 96 model–game–context comparisons, adjacent-round switching fell from 63.8% to 18.9%, and 71 comparisons stabilized after correction while five reversed.The follow-ups distinguish fixed-history policy effects from closed-loop sensitivity to a late-layer component.Source: §1 · p. 1, Figure 1 · p. 2

2 Related Work

Related work distinguishes strategic competence and aggregate cooperation from within-trajectory policy persistence. The paper situates cheap talk and causal intervention as complementary ways to study whether messages stabilize repeated policies and how.

Strategic Decision-Making in LLMs

  • Prior work describes LLM strategic play as boundedly rational and heuristic, while cooperation-steering research commonly emphasizes welfare or equilibrium rather than individual policy persistence.Strategic simulation validity also depends on experimental design and opaque training choices.Source: Strategic Decision-Making in LLMs · p. 2

Behavioral Stability

  • Cross-run reliability differs from within-trajectory persistence, which stable population averages can conceal and which does not establish that an agent is cooperative.The unit of analysis is one agent’s evolving policy within a repeated interaction.Source: Behavioral Stability · p. 2

Strategic Communication

  • Cheap talk is costless and non-binding, may be informative under aligned interests, and remains understudied as a stabilizer across conflict and coordination settings.The design separates strategic content, generic text, attribution, and interaction with observed behavior.Source: Strategic Communication · p. 3

Causal Analysis of Internal Representations

  • Decodability probes do not establish output use; because an altered action changes later histories, the paper pairs output counterfactuals with closed-loop projection ablation.The latter tests behavioral consequences across regenerated play rather than only a changed logit.Source: Causal Analysis of Internal… · p. 3

3 Methods

The methods combine repeated symmetric games and a label-symmetric switching measure with controlled message counterfactuals and closed-loop activation interventions. The design uses matched histories and dyads to assess policy effects, uncertainty, probability drift, and trajectory sensitivity.

Experimental Design

  • Four symmetric 2 × 2 games vary payoff rank orders, and each is presented in neutral, business, environmental, social, team, or international-relations framing.Agents choose A or B; communication is simultaneous in information, non-binding, and does not alter payoffs.Source: Experimental Design · p. 3

Behavioral Stability Metric

  • Adjacent-round switching measures first-order action persistence, with the communication effect defined so positive values indicate stabilization and either action can count as persistent.The measure does not capture general predictability, strategic quality, or welfare, and nine transitions per agent limit the observation window.Source: Behavioral Stability Metric · pp. 3–4
  • Switching above one-half implies negative first-order autocorrelation regardless of action frequency; the authors report switching rather than horizon-censored run length.Below one-half, the autocorrelation sign depends on the action marginal.Source: Behavioral Stability Metric · p. 3

Model Selection

  • The study selects four open-weight 7–9B instruction-tuned models, approximately holding parameter count constant while retaining architectural and training-history differences.Open weights permit access to action probabilities and activations; reasoning-distilled checkpoints are excluded.Source: Model Selection · p. 4

Model Execution and Statistical Analysis

  • Primary simulations use temperature 0.8; complete-case analysis excludes 39 erroneous dyads, while dyad-level bootstrap intervals and p-values are corrected across 96 comparisons.Retaining fallback actions and partial trajectories changes none of the corrected significance classifications.Source: Model Execution and Statistical Analysis · p. 4

Mechanistic Follow-Up

  • Experiments 1–2 replay 20 communication-treatment dyads per cell under fixed histories; current-message conditions vary content and attribution, while history-by-message contrasts test conditioning by the partner’s last action.Current-message replay decomposes expected disagreement into probability drift and action uncertainty; Experiment 2 crosses partner action A/B with mutual-benefit/self-prioritizing messages.Source: Mechanistic Follow-Up · p. 4
  • Experiment 3 constructs a history-balanced policy-content direction from mutual-benefit and self-prioritizing messages in Qwen and Falcon, then tests its removal during action choices.The direction is built from held-out-split decision data; projection leaves message generation unchanged and paired trajectories share context and seed.Source: Mechanistic Follow-Up · pp. 4–5

4 Results

Cheap talk reduces adjacent-round switching across all four games, but the magnitude and direction vary across models and contexts. Stabilization coincides with more persistent AA play and higher payoffs, while several corrected reversals cluster in social or team framings.

Communication Reduces Action Switching

  • 63.8% to 18.9%: communication reduced mean switching by 44.9 percentage points (95% CI [44.1, 45.6]); 71 of 96 cells remained significant after correction.The direction was stabilizing in 81 cells.Source: Communication Reduces Action Switching · p. 5
  • Pooled switching reductions were 45.8 points in Prisoner’s Dilemma, 51.6 in Snowdrift, 38.7 in Stag Hunt, and 43.5 in Harmony, with every game-level interval excluding zero.Corrected stabilizing cells numbered 21/24, 19/24, 14/24, and 17/24, respectively.Source: Communication Reduces Action Switching · p. 5
  • Communication raised Action-A rates by 18.49–23.49 points, AA outcomes by 25.90–30.08 points, and mean payoff by 0.404–1.036 points per agent per round.The paper interprets these shifts as stabilization toward persistent AA play rather than arbitrary persistence on either action.Source: Communication Reduces Action Switching · p. 5

Model and Context Heterogeneity

  • Qwen and Granite stabilized all 24 cells, with reductions of 83.2 and 73.5 points; Gemma and Falcon declined by 14.5 and 8.3 points, with 23 stabilizing, five destabilizing, and 20 null cells between them.Both Gemma and Falcon aggregate intervals exclude zero.Source: Model and Context Heterogeneity · p. 5
  • Qwen and Granite no-message play often alternated on nearly every transition, with in-phase joint cycling common in Harmony and Snowdrift.The reported in-phase patterns are inconsistent with tit-for-tat reciprocity as the explanation for these cycles.Source: Model and Context Heterogeneity · p. 5
  • At least eight switches in nine transitions implies negative first-order autocorrelation regardless of action frequency; communication moved every model–game cell below the one-half threshold.A preference for one action label does not explain symmetric alternation; the authors leave open whether failure to repeat the last emitted action contributes.Source: Model and Context Heterogeneity · p. 5
  • Five corrected reversals occurred for Falcon in social Snowdrift and Harmony, Gemma in social Stag Hunt and Harmony, and Gemma in team Stag Hunt.The reversals show context can change both magnitude and direction.Source: Model and Context Heterogeneity · p. 5

5 Mechanistic Analysis

Across three mechanistic follow-ups, message content and attribution, recent partner behavior, and a late-layer component each help explain how communication relates to action persistence. The immediate and history-conditioned effects depend on model and partner history, while closed-loop interventions show trajectory sensitivity to the late-layer component.

Experiment 1: Current-Message Policy Replay

  • Qwen’s endogenous message reduces expected switching 21.12 points more than partner-formatted dummy text; decomposition separates reduced probability drift from reduced action uncertainty.For Qwen, these components are 4.22 and 8.72 points, respectively, for the partner message; generic text can sharpen action distributions, while strategic attribution additionally limits movement across rounds. Partner-formatted dummy text increases switching in every model, and immediate specificity is strongest in Qwen.Source: Experiment 1: Current-Message Policy… · pp. 5–6, Figure 2 · p. 7

Experiment 2: History-Conditioned Message Effects

  • Recent partner action conditions message effects across models: pooled history-by-message interactions are corrected-significant, while conditional SP-minus-MB contrasts can reverse sign.Conditioning appears early and persists rather than accumulating monotonically; Qwen is positive at eight of nine transitions.Source: Experiment 2: History-Conditioned… · p. 6

Experiment 3: Layerwise Causal Intervention

  • From about layer 18, the learned direction produces larger, consistently positive held-out A–B logit-margin responses than equal-norm random directions.The closed-loop ablation results establish sensitivity of complete trajectories to this component, not unique mediation of communication-induced stabilization.Source: Experiment 3: Layerwise Causal… · pp. 6–7
  • At Qwen layer 22, switching rises from 6.0% under clean play to 70.0% under ablation (∆= 0.640 [0.553, 0.727]), with significant increases at layers 20, 22, and 24 in both models.Falcon remains significant at layer 26; neither model is corrected-significant at layer 28.Source: Experiment 3: Layerwise Causal… · pp. 6–7
  • Closed-loop projection lacks equal-norm random-direction controls, so ablation establishes component sensitivity, not projection specificity; message semantics also differ in favored action.The authors therefore do not claim unique mediation of communication-induced stabilization.Source: Experiment 3: Layerwise Causal… · p. 7

6 Conclusion

Across four repeated games, cheap talk generally reduces adjacent-round switching, though effects vary by model and context. Mechanistic findings point to message content, attribution, recent partner behavior, and a late-layer component, with causal and generalization claims bounded by the study’s design.

6 Conclusion

  • Across four repeated games, cheap talk reduces average adjacent-round switching from 63.8% to 18.9%, with 71 of 96 cell-level effects remaining stabilizing after correction.Effects vary sharply by model and context, with five reversals in social or team framings.Source: §6 · p. 7
  • Mechanistic analyses indicate that content and partner attribution jointly affect Qwen’s action uncertainty and probability drift, while recent partner behavior conditions message-framing effects across models.Removing a late-layer policy-content component increases switching during regenerated play in Qwen and Falcon.Source: §6 · p. 7
  • The causal result establishes trajectory sensitivity, not projection specificity or unique mediation; the study’s model, game, horizon, and intervention scope also limit generalization.Activation interventions cover depth-matched Qwen and Falcon in Prisoner’s Dilemma, and generalization to larger or reasoning-focused models, longer horizons, richer games, and alternative communication protocols remains open.Source: §6 · p. 7

SUPPLEMENTARY MATERIAL

The supplement expands the behavioral results and documents the study’s scope, analyses, and evidence of systematic alternation without communication.

A Scope and Analysis Inventory

  • The supplement covers four ten-round games across six contexts, with 100 dyads per model–game–context–treatment cell, and describes three mechanistic experiments.These include current-message replay, history-conditioned message effects, and layerwise causal interventions in Qwen and Falcon Prisoner’s Dilemma.Source: A Scope and Analysis Inventory · p. 10

A.1 Behavioral Outcomes and Payoffs

  • Behavioral outcomes are calculated within model–context cells and then equally weighted across 24 cells, with dyad-level bootstrap intervals.Communication and no-communication dyads are resampled independently because they are separate trajectories.Source: §A.1 · p. 10
  • Communication increases Action-A frequency by 18.49–23.49 percentage points and average payoff by 0.404–1.036 points per agent per round, alongside more AA outcomes.The magnitude is model-dependent; Qwen and Granite move strongly toward A in every game, while Falcon and Gemma change little in Stag Hunt and Harmony.Source: §A.1 · p. 10

A.2 Period-Two Cycling

  • Without communication, 91.5% of Qwen agents and 83.2% of Granite agents switch on all nine transitions, with median period-two adherence equal to one in every model–game cell.In-phase perfect alternation occurs in 73.4% of Qwen and 59.0% of Granite Harmony dyads, and 88.2% and 79.7% of their Snowdrift dyads.Source: §A.2 · p. 10

A.3 Error Audit

The supplement audits the behavioral sample and details how action policies, counterfactual message conditions, and uncertainty in the estimates are handled.

A.3 Error Audit

  • Of 19,200 planned dyads, 39 contain malformed output; the complete-case analysis retains 19,161 dyads and 344,898 transitions, with mean switching falling from 0.6377 to 0.1889.After correction, 71 of 96 contrasts are stabilizing and five destabilizing; including fallback actions and partial trajectories changes none of the corrected classifications.Source: §A.3 · p. 11

A.4 Policy Extraction

  • At each realized decision, replay scores the model’s binary action policy from returned log probabilities for A and B, renormalized over those two actions.This isolates relative preference between the valid actions while excluding probability mass assigned to formatting or explanatory tokens.Source: §A.4 · pp. 11–12
  • When an action token falls outside the returned top-20 window, the analysis uses the identification-interval endpoint nearest P(A) = 0.5, conservatively limiting policy extremity.This affected 0.59% of replay rows overall, with rates varying by model.Source: §A.4 · p. 13

A.5 Pairing and Inference

  • Inference for Experiments 1 and 2 pairs measurements within decision contexts, aggregates them by dyad, and bootstraps dyads within fixed game–context strata.Experiment 3 uses context-level t intervals for one-step slopes and paired trajectory differences for closed-loop tests, with correction applied by prespecified testing family.Source: §A.5 · p. 13

B.1 Counterfactual Construction

  • For Experiment 1, seven counterfactual prompts hold the realized history and other inputs fixed while varying the current text block and its displayed speaker role.Cross-attribution conditions separate message content, true authorship, and apparent conversational role.Source: §B.1 · p. 13, Table S6 · p. 14

B.2 Expected Policy Switching and Decomposition

  • Expected switching separates squared between-round change in P(A), or probability drift, from the adjacent policies’ Bernoulli action uncertainty.The no-message-minus-condition contrast is positive when the condition lowers policy-implied switching.Source: §B.2 · pp. 13–14

B.3 Results and Strategic Specificity

The results show that message effects depend on content, apparent source, and recent partner behavior, with patterns differing across models.

B.3 Results and Strategic Specificity

  • For Qwen, endogenous partner content is 21.12 percentage points [19.99, 22.22] more stabilizing than dummy content under matched partner framing.Under matched dummy content, plain presentation is 15.57 points [14.59, 16.53] more stabilizing than partner-attributed presentation; the pattern reflects interaction between content and apparent source.Source: §B.3 · p. 14
  • Both matched contrasts are positive in every model: real content improves persistence under partner framing, while partner framing reduces persistence for irrelevant content versus plain presentation.Partner framing is therefore consequential but not generically stabilizing; Qwen and Falcon also show a positive endogenous partner-message effect relative to deleting the message.Source: §B.3 · p. 14
  • For Qwen’s endogenous partner message, reduced probability drift contributes 4.22 points of its 12.94-point total stabilizing effect, while reduced action uncertainty contributes 8.72 points.Dummy text yields 0.95 points of drift reduction and 6.44 points of uncertainty reduction; Falcon’s effects are dominated by lower uncertainty, while Gemma and Granite show no positive total effect for endogenous partner messages.Source: §B.3 · p. 14, Figure S2 · p. 15

C.1 Matched History–Message Design

  • Experiment 2 crosses the partner’s latest action, A or B, with a current message expressing mutual benefit or self-prioritization.Synthetic prior-outcome blocks define the manipulation at every round while other listed inputs remain paired.Source: §C.1 · p. 16, Table S8 · p. 16

C.2 History-by-Message Estimand

  • The history-by-message estimand is half the conventional 2 × 2 difference-in-differences; a nonzero value means message-framing effects depend on recent partner action.The scale is retained as an average difference.Source: §C.2 · p. 16

C.3 Pooled and Game-Specific Results

History-by-message effects vary with the partner’s latest action, and their pooled components differ across models. The interaction appears early and persists, with model-dependent timing and magnitude.

C.3 Pooled and Game-Specific Results

  • The pooled interaction is positive in all four models, but the self-prioritizing-minus-mutual-benefit switching contrast reverses sign across partner histories.The after-A and after-B contrasts are 3.20 and −3.64 points for Qwen, 39.79 and −0.80 for Falcon, 11.90 and −24.32 for Gemma, and 19.91 and −12.70 for Granite; Qwen’s 3.42-point interaction is not distinguishable from zero in Snowdrift, while the other models are positive in all four games.Source: §C.3 · p. 16, Table S9 · p. 17

C.4 Components and Round Profile

  • Action uncertainty is the dominant common component, while probability drift contributes more in Gemma and Granite than in Qwen and Falcon.Drift and uncertainty contribute 0.53 and 2.89 points for Qwen, 0.45 and 19.84 for Falcon, 5.45 and 12.66 for Gemma, and 7.24 and 9.07 for Granite.Source: §C.4 · p. 16, Figure S3 · p. 16
  • Across transitions ending at rounds 2–10, the interaction appears early and persists, with model-dependent timing and magnitude.Qwen is positive at eight of nine transitions but unresolved at round 3; Falcon remains strongly positive, while Gemma and Granite are largest early before settling to smaller positive values.Source: §C.4 · p. 16

D Experiment 3: Layerwise Causal Intervention

The experiment constructs a history-balanced message-content direction and tests it with immediate steering and closed-loop projection ablation in depth-matched Qwen and Falcon models. Ablation increases switching in a late-layer band, with model-dependent peaks.

D.1 Depth-Matched Activation Capture

  • The intervention uses Qwen and Falcon, the only depth-matched pair, both with 28 layers, and captures ten Prisoner’s Dilemma communication trajectories per context for each model.Granite and Gemma have 40 and 42 layers, respectively; the matched depths allow the same layer grid without implying the candidate mechanism is absent in those models.Source: §D.1 · p. 17

D.2 History-Balanced Policy Direction

  • At each layer, the candidate direction is the difference between mutual-benefit and self-prioritizing message-class mean activations, balanced across partner-A and partner-B histories.Construction and held-out decisions are split by complete decision key so a decision cannot define and evaluate the direction.Source: §D.2 · p. 17

D.3 Immediate and Closed-Loop Tests

  • The one-step test adds the candidate direction at the final prompt position and compares its A–B logit-margin slope with an equal-norm random-direction slope; closed-loop ablation removes the component at every action choice.Closed-loop clean and ablated trajectories share model, context, and seed, while message generation remains unchanged; only the additive test includes the random-direction comparison.Source: §D.3 · p. 17

D.4 Layerwise Interpretation

  • Projection ablation significantly increases closed-loop switching at layers 20, 22, and 24 in both models and at layer 26 in Falcon, with neither model showing a corrected effect at layer 28.Qwen peaks at layer 22 (∆S = 0.640 [0.553, 0.727]); Falcon peaks at layer 20 (∆S = 0.581 [0.487, 0.674]) and remains positive at layer 26 (∆S = 0.306 [0.212, 0.401]). Excluding parser-fallback pairs leaves the corrected conclusions unchanged.Source: §D.4 · p. 18, Figure S4 · p. 18

E Additional Experiment 1 Display

Figure S5 displays current-message replay estimates across games and contexts, while Table S10 presents the Experiment 3 layer sweep.

Additional Experiment 1 Display

  • Table S10 reports the Experiment 3 layer sweep with one-step learned-minus-random logit-margin slopes and closed-loop ablated-minus-clean switching changes.Bold entries mark q < .05 after separate Benjamini–Hochberg correction across fourteen layers within each model and outcome.Source: Table S10 · p. 19
  • Figure S5 shows each current-message estimate as the reduction in open-loop expected adjacent-round switching versus no message, averaged equally over four games and six contexts.Positive values indicate greater policy persistence; intervals are 95% paired stratified-bootstrap confidence intervals based on 20 dyads per stratum.Source: E Additional Experiment 1 Display · p. 18, Figure S5 · p. 19

F Reproducibility Details

The supplement documents code, models, simulation settings, prompts, and analysis procedures. It also records an unresolved action-label and presentation-order robustness question.

F.1 Code and Data Organization

  • The released notebooks and analysis scripts organize three stages: behavioral trajectories, message and history counterfactuals, and layerwise causal interventions.Shared functions are under src/cheaptalk/, and the requirements files specify the released analysis and Experiment 3 environments.Source: §F.1 · pp. 19–20

F.2 Models and Software

  • Behavioral experiments use Qwen 2.5 7B and Falcon 3 7B in Experiments 1–3, and Granite 3.3 8B and Gemma 2 9B in Experiments 1–2; Experiment 3 reloads Qwen and Falcon GGUF weights into corresponding Transformers architectures.Behavioral and policy-replay calls use an 8,192-token context window. The original behavioral runs did not retain a complete package and GPU snapshot.Source: §F.2 · p. 20

F.3 Decoding and Randomness

  • Behavioral calls use temperature 0.8 and top-p 1.0 without an explicit Ollama seed, while Experiment 3 seeds its random generators and pairs clean and ablated trajectories by seed.Closed-loop pairs share model, context, and seed, yielding 60 paired trajectories per model and layer.Source: §F.3 · p. 20

F.4 Message-Exchange Protocol

  • Messages are composed from histories through the previous round, buffered until both are written, then revealed before action choices are generated with counterpart actions hidden.Execution is sequential, but the information flow introduces neither a first-mover message nor a within-round response message.Source: §F.4 · p. 20

F.5 System-Prompt Construction; Context framings

  • The 48 behavioral prompt templates combine one of six context framings, a treatment block, game payoff lines, and a shared ending, with agent identifiers substituted at runtime.The appendix supplies example competitive, social, team, diplomatic, business, and environmental framings.Source: §F.5 · p. 20, Context framings · p. 21

Treatment and game blocks

  • The communication treatment permits one short, non-binding message before each A/B action, whereas the no-communication treatment proceeds directly to the action phase.The common prompt ending requires an A-or-B action and says the final round is not announced in advance.Source: Treatment and game blocks · pp. 21–22

F.6 Round Prompts and Parsing

  • Primary analyses exclude error-marked or incomplete dyads; action parsing accepts A or B or selects the first standalone valid letter, otherwise defaulting to B and recording an error.An accumulated error terminates the dyad after the current round is scored.Source: §F.6 · p. 22

F.7 Counterfactual and Causal Details; F.8 Action Labels and Presentation Order

  • Experiments 1–2 replay message and history counterfactuals along fixed earlier histories, while Experiment 3 builds a direction on one decision-key split and tests it on held-out decisions.Experiment 3 compares one-step steering with an independent random vector and ablates the candidate direction during closed-loop play; action labels, option order, and payoff-line order were not counterbalanced, leaving a robustness question unresolved.Source: §F.7 · p. 22, §F.8 · p. 22
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