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Discovering Cooperative Pipelines: Autoresearch for Sequential Social Dilemmas

Víctor Gallego

arXiv:2605.30003v1cs.MAcs.AIcs.LG

TL;DR

Designing the pipeline that synthesizes LLM policies for multi-agent social dilemmas has largely remained a manual problem. This paper uses an outer-loop coding agent to autonomously redesign and evaluate that inner-loop pipeline, reliably outperforming hand-designed and prompt-only approaches while discovering objective-dependent strategies.

  • Problem

    Prior work tuned the many pipeline choices governing LLM-synthesized policies by hand, motivating whether an AI agent can design the pipeline.

  • Method

    An outer-loop researcher agent edits and evaluates an inner-loop LLM policy-synthesis codebase, retaining changes that improve a fixed welfare objective.

  • Results

    Across Cleanup and Gathering, autoresearch reliably exceeds hand-designed baselines, outperforms prompt-only optimization, and converges to qualitatively distinct objective-specific strategies.

  • Takeaways & Limitations

    The results support an information-design interpretation in which welfare objectives shape whether the researcher reveals efficiency-oriented or fairness-oriented coordination structure.

  • Takeaways & Limitations

    Because one shared program controls all agents, the setup evaluates joint coordination rather than equilibrium behavior under individual rationality.

Abstract

from arXiv · show

We study two-level autoresearch for cooperation: an outer-loop AI agent autonomously redesigns the inner-loop pipeline of an LLM policy-synthesis system for multi-agent Sequential Social Dilemmas (SSDs). A researcher agent $\mathcal{R}$ (run as a coding agent) reads the inner-loop source code, edits system prompts, feedback functions, helper libraries, and iteration logic, runs evaluations, and decides what to keep, following the autoresearch paradigm. Across two games (Cleanup and Gathering), two policy-synthesizer LLMs, and two welfare objectives (utilitarian efficiency and Rawlsian maximin), the researcher reliably exceeds hand-designed baselines, sharply tightens run-to-run variance, and outperforms prompt-only optimization. The discovered pipelines are objective-dependent: only under maximin does the researcher inject an explicit fairness mechanism into synthesizer pipelines, a class of mechanism that is absent from its own objective-agnostic system prompt and from every efficiency-optimized pipeline. This supports an information-design reading in which the researcher chooses what to reveal to the boundedly rational synthesizer as a function of the welfare objective. Code at https://github.com/vicgalle/autoresearch-social-dilemmas.

1 Introduction

The section frames LLM policy-synthesis pipelines for Sequential Social Dilemmas as an underexplored design problem and introduces a two-level autoresearch framework to optimize them. It evaluates this approach across SSD benchmarks, policy LLMs, welfare objectives, and realistic discovery constraints.

  • Motivation: Sequential Social Dilemmas turn individually rational play into collectively suboptimal outcomes in temporally rich multi-agent Markov games.The passage identifies pollution, over-harvesting, and open conflict as examples, while noting MARL difficulties from credit assignment, non-stationarity, and large joint action spaces.
  • Motivation: The inner-loop pipeline exposes design choices in prompts, feedback variables, helper functions, and refinement steps that materially affect synthesized policies.Prior work tuned these parameters by hand, motivating whether an AI agent can design the pipeline.
  • Framework: A two-level autoresearch framework lets an outer-loop coding agent edit an inner-loop policy synthesizer, evaluate held-out seeds, and retain changes improving a fixed welfare objective Φ.The researcher operates in an ordinary git repository using code reading, diffs, shell commands, and standard CLI/git scaffolding.
  • Evaluation setting: The discovery process operates under noisy multi-seed evaluations, stochastic code generation, bounded evaluation budgets, and a heterogeneous repository requiring end-to-end navigation.These conditions are presented as resembling those faced by a deployed discovery agent, despite the SSDs being gridworld benchmarks.
  • Scope: The study spans Cleanup and Gathering, two policy LLMs, and utilitarian efficiency U and Rawlsian maximin min_i R_i welfare objectives.The contributions describe this as the first autoresearch instantiation in a multi-agent decision-making domain.

2 Background

The paper frames Sequential Social Dilemmas as partially observable Markov games with temporal cooperation challenges, and studies Cleanup and Gathering under efficiency and Rawlsian maximin objectives. Its symmetric, code-based LLM policy-synthesis setup turns the strategic problem into joint coordination while exposing feedback and pipeline design to automated search.

  • SSD formalism: Sequential Social Dilemmas are partially observable Markov games in which agents must learn when and where to cooperate, not merely whether to cooperate.They include agents, states, action spaces, transitions, rewards, and a finite episode horizon.
  • Benchmark dilemmas: Cleanup models costly public-goods provision, whereas Gathering models a common-pool resource in which aggression can monopolize resources and reduce welfare.Cleanup has N=10 agents; Gathering has N=4.
  • Benchmark dilemmas: Both games use 8–9 discrete actions and H=1000-step episodes, contrasting asymmetric provision costs with symmetric restraint temptations.In Cleanup, cleaners pay while all benefit; in Gathering, every agent faces the same temptation.
  • Objectives and metrics: The study evaluates social outcomes including mean positive-reward timing, active survival, and Rawlsian maximin welfare, mini Ri, which optimizes the worst-off agent’s return.Higher mean collection time indicates that resources were preserved later.
  • Policy-synthesis setup: A single shared Python policy π controls all agents, reframing the classical dilemma as joint coordination and scheduling toward an explicit welfare objective.Because π receives agent_id, shared source code can still produce differentiated roles and time-rotated duties.
  • Policy-synthesis setup: The frozen LLM synthesizer revises executable code from prior policy source and evaluation feedback, while the broader framework automates choices about feedback content and pipeline configuration.Policies access full environment state and helper libraries, enabling rich coordination logic in algorithm space.

3 Two-Level Framework

The paper introduces a two-level framework in which a researcher agent searches over the full codebase of an LLM policy-synthesis pipeline to optimize a chosen welfare objective. This structure also supports a mechanism-design interpretation: the researcher controls the information, tools, and feedback incentives presented to a boundedly rational policy synthesizer.

  • Two-Level Architecture: The researcher agent autonomously modifies the inner-loop pipeline as a designable artifact, proposing changes, evaluating outcomes, and refining the running-best configuration.The architecture is general to pipelines where an LLM generates artifacts, evaluates them, and iterates.
  • Configuration Space: Each configuration c = (p, ϕ, H, ι) specifies the system prompt, feedback construction, helper-function library, and iteration logic.Iteration logic includes the number of inner iterations and sampling strategy.
  • Inner-Loop Evaluation: The inner loop repeatedly synthesizes, validates, and evaluates LLM policies, while held-out evaluation maps each configuration to a scalar score under a fixed welfare functional Φ.Validation includes AST-based safety checks and a smoke test; evaluation produces reward and social-metric outcomes.
  • Welfare Objectives: The framework optimizes either utilitarian efficiency ΦU, which rewards collective throughput, or Rawlsian maximin Φmin, which prioritizes the worst-off agent.The two objectives impose different distributional priorities on cooperation costs.
  • Mechanism-Design Interpretation: The researcher functions as a mechanism designer by controlling the information structure, available helper functions, and feedback incentives under which the synthesizer operates.Because synthesizer effectiveness depends on the information and tools provided, the authors characterize the task as closer to information design.

4 Experiments

Across 12 autonomous runs, autoresearch consistently improves welfare over hand-designed and prompt-only baselines in Cleanup and Gathering. The discovered pipelines depend on both game structure and welfare objective, introducing explicit fairness mechanisms for maximin in Cleanup but not efficiency optimization.

  • Experimental design: 12 autonomous researcher runs span two policy LLMs, two Cleanup objectives, and one Gathering objective, with two replications per condition.The researcher edits and evaluates a real Python codebase without human intervention.
  • Main results: U ≈3.1–3.2 on Cleanup and U ∈ [2.47, 2.52] on Gathering, substantially exceeding hand-designed baselines and outperforming prompt-only optimization.Cleanup baselines are 1.93 for Gemini and 0.86 for Sonnet; Gathering baselines span 0.03–2.42.
  • Objective-dependent outcomes: 1% efficiency loss under Gemini maximin optimization raises equality from E=0.55 to 0.98 while transforming deeply negative baseline maximin welfare into mini Ri = 290.The discovered mechanism is fair duty rotation using agent_id and env._step_count.
  • Game-dependent outcomes: Game structure determines fairness requirements: Cleanup needs maximin optimization to reach E > 0.9, while symmetric Gathering reaches E > 0.94 through efficiency optimization alone.Cleanup baseline equality ranges from E=0.04 to 0.62; therefore no separate Gathering maximin runs are needed.
  • Objective-dependent discovery: Gemini maximin pipelines include explicit fairness mechanisms in 4/4 runs, whereas efficiency pipelines include them in 0/4 runs despite independent discovery.The researcher-authored rotation template appears only under Φmin, although its system prompt is identical across objectives and contains no objective-conditional guidance.
  • Failure modes and safeguards: Three recurring failure modes—over-prescription, iteration regression, and feedback overload—account for most discarded iterations, while final pipelines showed no inspected spec-gaming patterns.The reported spec-gaming inspection found spatial heuristics, state queries, metric-threshold interventions, and increasing |S| rather than seed-specific hard-coding.

5 Related Work

The paper situates its contribution among SSD cooperation research, LLM program synthesis, reflection-based optimization, and automated AI research. Its distinctive focus is an outer coding agent that rewrites the pipeline for multi-agent policy synthesis rather than optimizing only policies, prompts, or single-agent systems.

  • Sequential social dilemmas: The work complements SSD cooperation research by automating cooperative-program search instead of evolving neural policies.SSDs include Gathering and Cleanup, with established social outcome metrics U, E, S, and P.
  • LLMs for policy and program synthesis: Unlike prior LLM synthesis systems targeting single-agent control or non-strategic optimization, the outer agent rewrites the synthesis pipeline itself.The inner loop builds on Gallego, while this work operates one level above it.
  • LLM reflection and prompt optimization: The framework extends reflection and prompt-optimization methods by modifying the system prompt, feedback construction, helper library, and iteration logic together.Prompt optimization is therefore treated as one component of a broader pipeline.
  • Automated AI research: The system shares autoresearch’s coding-agent, frozen-evaluation-harness, and diff-based-history architecture but applies it to multi-agent policy synthesis rather than nanoGPT pretraining.Karpathy’s autoresearch rewards validation loss, whereas this system targets a different inner loop and objective.
  • Automated mechanism and information design: The outer agent resembles automated mechanism and information design by selecting information for boundedly rational synthesizers, without treating the synthesizer as strategically deceptive.Classical mechanism design uses explicit incentive constraints, while information design studies signaling policies that shape receiver behavior.

6 Discussion and Conclusion

The two-level framework autonomously discovers improved LLM-policy pipelines, reliably surpassing hand-designed baselines and converging on similar strategies within each game–objective condition. Results support an information-design interpretation: the researcher reveals efficiency-oriented or fairness-oriented structure according to the welfare objective.

  • Discussion and Conclusion: The coding agent autonomously discovers pipeline configurations that improve an inner-loop LLM system and reliably exceeds hand-designed baselines across independent runs.Within each game–objective condition, it converges on qualitatively similar strategies without task-specific scaffolding beyond a standard CLI and git.
  • Mechanism design in action: Under ΦU, the researcher reveals efficiency-oriented information that guides productive but unequal role allocation, whereas under Φmin it adds fairness-oriented structure for egalitarian coordination.Examples include waste counts and zone assignments under ΦU, and rotation schedules and equity feedback under Φmin.
  • Human oversight: The architecture supports human oversight through an auditable git repository and a delegation boundary separating the human-defined welfare objective from the researcher’s implementation choices.The researcher operates autonomously, while the evaluation Φ specifies what to optimize.
  • Future work: Future work includes applying the framework to other LLM-driven pipelines, testing adversarial objectives for reward hacking, and extending it to asymmetric programs.Proposed domains include code optimization, scientific experiment design, and infrastructure tuning.

A Limitations

The study’s claims are bounded primarily by reliance on a single researcher LLM and by the fact that the inner-loop infrastructure is itself a designed artifact. The most important follow-up is to replicate the researcher ablation across multiple frontier coding agents.

  • Researcher dependence: The main experiments and Gemma appendix use only one researcher LLM: Claude Opus 4.6 through the Claude Code CLI.The authors identify a researcher ablation across multiple frontier coding agents, using the same fixed system prompt, as the single most important follow-up.
  • Infrastructure dependence: The inner-loop infrastructure is itself a designed artifact, so the claim that the researcher uses no task-specific scaffolding applies only to its tooling.The passage specifies that this tooling includes the CLI, git, and file edits.

B Additional Results

Additional results show that the researcher improves the full inner-loop output distribution rather than relying on lucky generations. In Cleanup, maximin optimization converts deeply negative worst-off outcomes into substantially positive values, while final metrics show objective-dependent welfare differences.

  • Maximin outcomes: All four Cleanup maximin-optimized runs transform deeply negative baselines into substantially positive mini Ri values.Gemini reaches ∼290, while Sonnet reaches ∼160–200; mini Ri = 0 marks the point where no agent loses reward overall.
  • Maximin outcomes: Final Cleanup maximin optimization achieves mini Ri +290 for Gemini or +179 for Sonnet, versus approximately −200 under efficiency optimization.The figure describes this as the sharpest contrast among the final metrics.
  • Inner-loop robustness: The whole inner-loop output distribution improves, not just its tail, indicating that gains are not driven solely by lucky generations.Figures 5 and 6 average metrics across all inner iterations and show trajectories ramping at essentially the same rate, with only mild attenuation.
  • Inner-loop robustness: Cleanup mean maximin reaches mini Ri ≈200–275 across inner iterations, compared with final-run values of 179–290.This agreement supports broad-based improvement across the inner-loop trajectory rather than improvement confined to the kept output.

B.1 Discard Taxonomy · B.2 Spec-gaming inspection

Across 100 outer iterations, discards were strategic objective regressions rather than code-validity failures, while all-inner-iteration averages closely tracked the kept-policy gains. Inspection found thresholded, metric-tied feedback and larger sample sets rather than held-out-evaluation spec-gaming, with over-prescription the closest observed behavior.

  • B.1 Discard Taxonomy: Across 12 runs, R made 100 outer iterations: 7 baselines, 47 kept, and 46 discarded.Kept iterations satisfied Jj > J∗+ τ with τ=0.
  • B.1 Discard Taxonomy: Mean efficiency across all inner iterations tracked the kept-policy trajectories closely, indicating gains across the inner-loop output distribution.The comparison covered Cleanup (N=10) and Gathering (N=4).
  • B.1 Discard Taxonomy: Mean maximin across all inner iterations lifted deeply negative baselines to ∼200–275, only mildly below kept-policy values.This result covered the 4 Cleanup Φmin runs, with the dashed reference at mini Ri = 0.
  • B.1 Discard Taxonomy: No outer iteration was discarded for AST safety or smoke-test failure, separating code-validity issues from outer-loop strategy decisions.The AST-and-smoke-test guard and regeneration-on-error formed a non-leaky boundary.
  • B.1 Discard Taxonomy: Named failure modes accounted for 23/46 (50%) of discards, while 20/46 (43%) were pure regressions on J.Pure regressions followed intuitively plausible modifications that underperformed the running best J∗.
  • B.2 Spec-gaming inspection: R’s feedback edits were thresholded interventions on the optimized metric, such as a “REGRESSION” guard for latest U below running-best U and a “PROBLEM” alert when maximin < 0.The configuration tuple c = (p, ϕ, H, ι) allowed unrestricted edits to the helper library and feedback function in principle.
  • B.2 Spec-gaming inspection: These feedback conditions used the primary scored signal and natural metric-scale thresholds, while increasing |S| from 5→8→12 when chasing maximin reduced seed-noise.The closest observed behavior to spec-gaming was over-prescription, where detailed worked examples caused M to effectively copy them.

B.3 Smaller Open-Weight Model: Gemma 4 26B

With Gemma 4 26B-A4B-IT, the framework recovers substantially from complete failure, but performance depends sharply on the game and welfare objective. Maximin optimization outperforms direct efficiency optimization on Cleanup, while Gathering nearly matches frontier models.

  • Gemma 4 26B-A4B-IT was evaluated in three runs: Cleanup under efficiency and maximin objectives, and Gathering under efficiency, with Opus 4.6 as researcher R.
  • U=−10.0 on Cleanup and U=0.0 on Gathering mark complete baseline failure, from CLEAN-spam behavior and broken BFS calls, respectively.The researcher ran Jmax=10–18 outer iterations per condition.
  • U=0.87 under efficiency optimization recovers Cleanup performance but remains far below frontier models at U≈3.2.The discovered pipeline uses K=1 and highly structured worked examples with explicit cleaning-role assignment.
  • U=1.71 under maximin optimization exceeds direct efficiency optimization’s U=0.87, alongside E=0.94 and mini Ri=137 on Cleanup.The objective induces rotating cleaning duties and index-based apple assignment; frontier models instead yield U≈3.1–3.2 under both objectives.
  • For weaker models, maximin may optimize overall social welfare better than direct efficiency by enforcing coordination that compensates for difficulty implementing complex strategies.The passage attributes this effect to structured coordination serving as a scaffold for the weaker model.
  • U=2.44 on Gathering, with E=0.98 and mini Ri=580, nearly matches frontier models after 10 outer iterations, with four configurations kept.The researcher discovers Voronoi partitioning and respawn-aware camping, using K=5 for sufficient refinement.

B.4 Compute Requirements … C.3 System prompt p: from neutral framing to strategic briefing

The appendix quantifies autoresearch compute and traces how a fixed researcher prompt produces objective-dependent, researcher-authored pipeline artifacts. These artifacts range from geometry-matched coordination helpers to strategic policy prompts that explicitly encode maximin fairness but not efficiency.

  • B.4 Compute Requirements: Policy LLM generation consumed 86–97% of inner-loop time, while the researcher agent consumed 41% of total wall-clock time, or 25.6h of 62.2h.Inner-loop evaluations combine 2–3 policy-generation calls with 5–12 simulation seeds; Sonnet evaluations took approximately twice as long as Gemini.
  • C Researcher-Authored Pipeline Artifacts: Appendix C organizes final-commit excerpts by artifact type, contrasting configurations across objectives and games, with C.1 presenting the researcher prompt upstream of the remaining artifacts.The configuration is c = (p, ϕ, H, ι), authored by researcher R to produce the inner-loop outputs.
  • C.1 Researcher system prompt pR: The researcher is Claude Opus 4.6 via Claude Code CLI and uses one fixed system prompt across runs, varying only the game name and efficiency-versus-maximin metric flag.The prompt defines the configuration space and evaluation harness rather than task-specific strategic guidance.
  • C.1 Researcher system prompt pR: pR omits time-based role rotation and objective-conditional strategy guidance, despite allowing exploration of prompt, feedback, helper, and iteration modifications.Its closest strategic suggestion is static role assignment, not time-rotated duty.
  • C.2 Helper library H: coordination primitives: The researcher adds black-box helpers for state inspection and coordination, including waste or yield scoring, zone assignment, and role rotation.These primitives spare the policy LLM from reimplementing difficult logic on each iteration.
  • C.2 Helper library H: coordination primitives: Helper complexity follows game geometry: row-bands suffice for Cleanup maximin fairness, whereas Gathering requires wall-aware BFS-Voronoi territory ownership.The researcher selects the simpler primitive whenever it works rather than fixing the helper type in advance.
  • C.3 System prompt p: from neutral framing to strategic briefing: Under maximin, the researcher expanded the neutral 165-line API prompt into a 325-line strategic briefing centered on Rawlsian fairness, rotation, and apple zoning.The briefing warns against permanent cleaning roles, recommends time-based rotation, and instructs agents to collect within their zones when not cleaning.
  • C.3 System prompt p: from neutral framing to strategic briefing: The Gathering prompt follows a different axis, emphasizing self-play avoidance of BEAM and stepwise Voronoi partitioning rather than maximin rotation.These researcher-added insights match the policy implementation described for Gathering.

C.4 Feedback ϕ: adaptive diagnostics … D.2 Cleanup, Φmin (Gemini): time-rotated, geographically interleaved roles

The researcher discovers objective-dependent feedback, iteration settings, and policy mechanisms that stabilize effective runs and improve fairness. In Cleanup, efficiency favors static low-index cleaners, whereas maximin favors rotating, spatially interleaved roles.

  • C.4 Feedback ϕ: adaptive diagnostics: Adaptive feedback becomes a state machine that repurposes the same metric to stabilize a working policy or redirect a failing one.Efficiency uses a stability guard at high U, while maximin injects fairness diagnostics when the worst-off agent loses reward.
  • C.4 Feedback ϕ: adaptive diagnostics: Thresholded feedback interventions help reduce run-to-run variance by preventing high-U regressions and injecting rotation hints in negative-maximin cases.The stability guard protects working policies from over-refinement, while the fairness alert recovers unfair policies.
  • C.5 Iteration logic ι: per-condition hyperparameters: In maximin Gemini, identical K=3, |S|=5 configurations produced mini Ri=295 on one seed set and mini Ri=100 on another.The researcher increased |S| from 5 →8 →12 until the seed-averaged signal stabilized.
  • C.6 Cross-artifact observations: Helpers provide non-trivial primitives while prompts select the strategy class; feedback is the only adaptive component that changes what the policy synthesizer sees.Prompts without helpers mentioned rotation without implementing it, whereas helpers without prompt updates often went unused.
  • C.6 Cross-artifact observations: The configuration c is a function of welfare objective Φ, and the best maximin Gemini diff totals ∼300 added lines across four files.Approximately 80 added lines appear in the listings, with the remainder consisting of API documentation and worked examples.
  • D Selected Generated Policies: Generated policies differ qualitatively between static and rotating Cleanup roles, illustrating the objective-dependent mechanisms highlighted in the paper’s findings.The selected listings are verbatim synthesizer outputs from the final inner-loop iteration, with repeated boilerplate elided.
  • D.1 Cleanup, ΦU (Gemini): static interleaved roles + dynamic threshold: The best efficiency Cleanup policy achieved U=3.25, E=0.61, and mini Ri=−182 using permanent low-index cleaners with a waste-dependent threshold.Higher pollution recruits more cleaners, but cleaner identities remain fixed, maximizing efficiency while imposing unequal costs.
  • D.2 Cleanup, Φmin (Gemini): time-rotated, geographically interleaved roles: The best maximin Cleanup policy achieved U=3.19, E=0.98, and mini Ri=296 using 50-step role rotation and spatially interleaved cleaners.The cleaner indices {1, 4, 8} are interleaved along the river so on-duty agents walk short distances to assigned slices.

D.3 Cleanup, Φmin (Sonnet): independent rediscovery of duty rotation · D.4 Gathering (Gemini): wall-aware Voronoi + spatiotemporal targeting · D.5 Cross-condition observations

Across Cleanup and Gathering, autoresearch independently discovers objective-specific coordination mechanisms: fair duty rotation for maximin Cleanup and spatial-temporal targeting for Gathering. Cross-condition results show welfare objectives shape role assignment, while independent LLM runs rediscover similar rotation structures.

  • D.3 Cleanup, Φmin (Sonnet): independent rediscovery of duty rotation: Best run reached U=2.93, E=0.83, and mini Ri=154 with phase-rotated cleaning and zone-rotated collection.A 50-step phase counter rotates two cleaners among ten agents, while a 200-step zone counter rotates five-row collection bands, ensuring structural fairness.
  • D.3 Cleanup, Φmin (Sonnet): independent rediscovery of duty rotation: A separate Sonnet maximin run instead used synchronized cleaning and collecting thresholds, reaching mini Ri=200 without an agent_id phase shift.Agents entered cleaning above waste_fraction(env) > 0.22 and collecting below 0.08.
  • D.3 Cleanup, Φmin (Sonnet): independent rediscovery of duty rotation: The rotation policy assigns exactly two cleaners per phase using (agent_id + phase) % n, while collectors cycle through spatial zones.The implementation uses 50-step phases for cleaning and 200-step zone phases for collection.
  • D.4 Gathering (Gemini): wall-aware Voronoi + spatiotemporal targeting: In Gathering, the best run achieved U=2.47, E=0.98, and mini Ri=580 through wall-aware Voronoi territories, centralized BFS, and spatiotemporal apple targeting.Because costs are symmetric, the discovered policy uses no role differentiation and instead optimizes spatial and temporal allocation.
  • D.4 Gathering (Gemini): wall-aware Voronoi + spatiotemporal targeting: The Gathering implementation scores reachable cells with exact wall-aware distances and prioritizes apples by earliest collection time, using max(walk_distance, respawn_timer).Alive apples are approached directly, while dead apples are targeted by camping on a safe adjacent cell.
  • D.5 Cross-condition observations: Gemini and Sonnet independently rediscovered (id + phase) % n duty rotation with similar phase lengths of T ≈50 steps in 3/4 maximin runs.The runs used separate dedicated git branches, supporting convergence across independent searches.
  • D.5 Cross-condition observations: Across conditions, static agent_id < τ maximizes U but harms mini Ri, whereas time-rotated (agent_id + step//T) % n maximizes mini Ri at ≤1% efficiency cost.The passage attributes the efficiency cost specifically to the Gemini results.
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