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MARL-BattleGrounds: A Novel JAX-native Benchmark for Heterogeneous and Competitive Multi-agent RL

Ulixes Tariq Hawili, Subramanian Ramamoorthy, Yoann Altmann, Ignacio Carlucho

arXiv:2610.14883v1cs.AIcs.LGcs.MA

TL;DR

MARL research benchmarks often trade rich team play against computational efficiency, leaving a gap between simple unit-micromanagement tasks and costly full games. MARL-BGs fills this middle with a JAX-native benchmark, coordination-focused game, evaluation modes, and research tools. Its first results show stronger teams combining abilities while key scenario and partner-coordination challenges remain.

  • Problem

    MARL benchmarks tend to be either fast and simple, reducing to unit micromanagement, or rich and costly, limiting access to deep team-play research.

    Source: §1 · p. 1

  • Method

    MARL-BGs provides a JAX-native heterogeneous team-vs-team benchmark with Team Deathmatch, canonical evaluation modes, detailed teamwork metrics, and research workflow tools.

    Source: §1 · pp. 1–2

  • Results

    Stronger teams combine abilities, yet no system solves an endgame scenario, learned agents partner poorly with strangers and humans, and an expert human beats the tournament winner.

    Source: §1 · p. 2, §9 · p. 9

  • Takeaways & Limitations

    MARL-BGs is built to measure open challenges in scenario solving, coordination with unfamiliar partners, and human-AI teaming.

    Source: §1 · p. 2, §9 · p. 9

    The reported LLM evaluation uses one small model with greedy decoding, no thinking, and no memory, while human-AI results comprise six games with one expert who could take unlimited time per move.

    Source: §8 · p. 8

Abstract

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We present MARL-BattleGrounds (MARL-BGs), an easy-to-use JAX-native benchmark for heterogeneous and competitive multi-agent reinforcement learning (MARL), designed to be sample-efficient, computationally efficient, and researcher-centric. MARL benchmarks are typically simple and efficient, like SMAX, where winning reduces to unit micromanagement, or rich and costly, like Dota 2. MARL-BGs fills this missing middle. Its first mode, Team Deathmatch, is a simultaneous turn-based game between two teams of five heterogeneous agents. The five classes have distinct basic, passive, and ultimate abilities designed to synergize with allies and counter enemies. Our 52 hand-designed maps with diverse obstacles include a 12-map curriculum and ten held-out validation and test maps. MARL-BGs provides two canonical evaluation modes. First, eight endgame scenarios form a hard generalization challenge: each asks a team to win an unseen, nearly lost position against a strong reactive controller within 5-10 ticks. Second, a monthly round-robin tournament retrains each submission on equal compute, plays it against every member of the current "Big Nine" field, and publishes the Elo results on the official leaderboard. All entrants are publicly released as downloadable opponents. MARL-BGs records 11,192 metrics per game in 28 topics. We also include three strong scripted opponents, an analytical replay viewer, and off-the-shelf tools for self-play, cross-play, curriculum learning, and zero-shot coordination evaluation. We even provide an API for LLM-based agents and use it to evaluate Qwen3.5-9B against our strongest policy. In our BattleClient, humans can play alongside or against any mix of policies, enabling human-AI evaluation. We benchmark MARL-BGs with six additional deep MARL baselines, which we release. On one RTX 5090 with 1,024 parallel games, the simulator runs 50,000 5v5 game steps per second.

1 Introduction

MARL-BGs fills the gap between simple, efficient MARL benchmarks and rich but costly games with a fast, heterogeneous team-vs-team benchmark. It combines a coordination-focused game, comparable evaluation modes, and tools for the research workflow, while early results expose open challenges in generalization and teamwork.

Design goals

  • MARL-BGs is designed to be sample-efficient, computationally efficient, and researcher-centric, with its game, evaluation, and tools forming the three contributions.The complete repository and Hugging Face models are planned for public release upon manuscript acceptance.Source: §1 · pp. 1–2

The Game

  • Team Deathmatch uses up to five agents per team, with hand-designed classes whose abilities require ally synergy and enemy counters across 52 obstacle maps.The game is partially observable and demands high-level coordination.Source: §1 · p. 2

Evaluation

  • The monthly tournament compares policies on held-out maps under equal budgets in mirrored 5v5 games, using draw-aware Elo and confidence intervals.Eight verified endgame scenarios test agent modeling and multi-step planning, while up to 11,192 metrics per game describe teamwork.Source: §1 · p. 2

Tools

  • The benchmark provides a workflow spanning six tuned baselines, scripted opponents, cross-play and zero-shot coordination tools, an LLM-agent API, human play, and game replay.Researchers can also evaluate arbitrary mixes of policies through one call.Source: §1 · p. 2

Season 0 results

  • Season 0 shows that stronger teams combine abilities, yet no system solves a scenario, learned agents partner poorly with strangers and humans, and an expert human beats the tournament winner.These open problems are what MARL-BGs is designed to measure.Source: §1 · p. 2

2 Related Work

The related-work comparison positions MARL-BGs as combining features that prior benchmarks do not bring together. It also identifies gaps in comparative evaluation and in tools for studying heterogeneous partners and human-AI play.

Evaluation gaps

  • Prior benchmarks lacked shipped rating tools with confidence intervals, held-out evaluation maps, and a broad set of verified scenarios.Official competitions were often short-lived, and detailed logs were not generally turned into full team metrics.Source: §2 · p. 2

Research tools

  • Existing coordination tools were limited for zero-shot partnerships, heterogeneous team play, and filling team slots with mixed learned, scripted, LLM, hybrid, or human players.The comparison notes that only two cited suites ship full zero-shot coordination tools, and that most benchmarks are purely cooperative.Source: §2 · p. 2

Benchmark comparison

  • No prior benchmark combines heterogeneous team-vs-team play in a fast JAX simulator with held-out maps, verified scenarios, a recurring rated tournament, and detailed teamwork metrics.The comparison covers sixteen benchmarks and games across twenty-two features.Source: §2 · p. 2

3 Preliminaries

Team Deathmatch is a simultaneous-action, two-team, zero-sum, partially observable game with deterministic transitions and sparse terminal rewards. The preliminaries also specify the action interface, observation constraints, and benchmark-feature table.

Game formulation

  • Each tick, agents choose legal actions from their observations simultaneously, and a deterministic transition updates the state; teams receive sparse win, loss, or draw rewards at game end.Games draw if scores are equal at 20 or the game remains open after 300 ticks.Source: §3 · p. 2

Action space

  • Each agent’s action has move, target, and Ultimate heads, with exact legal-action masks defining available choices.The baselines flatten these heads into 198 joint choices.Source: §3 · p. 2

Benchmark comparison

  • Table 1 groups benchmark features by family and marks each as present, partial, or absent.The supplementary material provides the rule and sources for every mark.Source: Table 1 · p. 3

Observations

  • By default, observations include visible agents and living teammates’ sensor rows, while a centralized critic may use the full state only during training.Messages arrive one tick after they are sent; actors never receive the full state.Source: §3 · p. 3

4 The Game: Team Deathmatch

Team Deathmatch is designed to support efficient experiments and researcher workflows while requiring coordinated play among heterogeneous agents. Its rules, class abilities, maps, and JAX API define the game and its use in research.

4.1 Design Goals

  • The pure-JAX simulator uses fixed array shapes and resets finished games independently, while exact action masks and optional curricula support sample-efficient training.Changing ordinary values such as maps or rosters does not force recompilation; the API and workflow tools support researcher-centric use.Source: §4.1 · p. 3

4.2 Rules

  • Teams may have one to five agents, and tournament games use mirrored 5v5 rosters; kills score points, with extra points for deaths in the victim’s Red Zone.Obstacles block sight and attacks, and agents respawn in five-tick waves with a three-tick spawn shield.Source: §4.2 · pp. 3–4

4.3 Five Classes

  • Each hand-designed class has a Basic ability, passive, and 30-tick-cooldown Ultimate, with strengths and weaknesses that call for ally support and counterplay.For example, the Priest is the only healer and cannot deal damage, while the Mage has the highest Basic damage and lowest health.Source: §4.3 · p. 4

4.4 Maps

  • The 52 mirrored 20 × 10 maps include 0–32 obstacles; maps 0–11 form a curriculum, maps 42–46 are held out for validation, and maps 47–51 for testing.No policy is tested on a map it was trained or selected on.Source: §4.4 · p. 4

4.5 API

  • The familiar JaxMARL-style API exposes make, reset, and step, and its explicit JAX state supports jit, vmap, and lax.scan.A single wrapper can turn JAX or host-Python methods into Systems without requiring a base class, model framework, or learner.Source: §4.5 · p. 4

5 The Evaluation: Scenarios, Tournament, Metrics

MARL-BGs evaluates teams through unseen endgame challenges and a fixed-field tournament, with metrics that expose teamwork beyond win rates. Its protocols use held-out scenarios and maps, while released entrants and checkpoints expand the pool of opponents.

5 The Evaluation: Scenarios, Tournament, Metrics

  • The evaluation also supports other team sizes and reports which systems, rosters, maps, and spawn ends produced each result.The evaluation pipeline allows scripted opponents at every stage.Source: §5 · p. 4, Figure 3 · p. 5

5.1 Mode 1: Endgame Scenarios

  • Eight hand-designed, nearly lost positions test whether a team can beat a strong reactive controller within 5–10 ticks on arenas unseen in training or selection.Each scenario has a verified winning line and tests team skills such as teammate and opponent modeling, sacrifice, and multi-step planning.Source: §5.1 · pp. 4–5, Table 2 · p. 5

5.2 Mode 2: The Official Tournament

  • The official tournament rates entrants against the Big Nine using mirrored 5v5 games on held-out test maps, with spawn ends swapped across paired games.A challenger trains once under a shared compute budget, plays every Big Nine member, and can replace the lowest-rated entrant; all entrants are released as downloadable opponents with checkpoints.Source: §5.2 · p. 5
  • The tournament rating uses a Bradley–Terry–Davidson model fit to all games and reported on an Elo scale centered at 1,200, with 95% intervals.A 200-Elo lead corresponds to winning about 76% of decisive games.Source: §5.2 · p. 5

5.3 Metrics

  • Full metrics provide 11,192 values across 28 topics, including teamwork, positioning, status effects, and ultimates; 81% record who did what to whom.Researchers can choose none, priority (16 values per game), or full metric storage.Source: §5.3 · p. 5, Figure 4 · p. 6

6 The Tools

MARL-BGs supplies opponents, learners, and workflow tools for studying competitive and cooperative MARL. Its interfaces also support LLM agents and human-AI evaluation.

Opponents and learners

  • The benchmark includes six deep MARL baselines and three deterministic scripted opponents whose observations match those available to learned actors.Released baseline families include MAPPO, IPPO, QMIX, and PQN with VDN value mixing.Source: §6 · p. 6

Ready-made research setups

  • Researchers can configure self-play, opponent pools, mixed teams, curricula, frozen partners, and cross-play, with native support for zero-shot coordination and ad hoc teamwork.Custom or built-in reward shaping affects the learner’s training signal, not actors’ inputs or the official score.Source: §6 · p. 6

LLM-agent API

  • The LLM API turns a language model behind a Chat Completions endpoint into a System, checking its JSON action against the legal-action mask.LLM agents and planners can play without a per-turn time limit; only official leaderboard entries must run as pure JAX.Source: §6 · p. 6

Clients

  • The BattleClient lets people play alongside or against policies, while the Replay Viewer supports tick-by-tick inspection from the full view or an agent’s point of view.Replay panels show agent observations, choices, and metrics, including who did what to whom.Source: §6 · p. 6

7 Experiments

Season 0 experiments measure simulator and training costs, baseline performance, and team behavior across scenarios, LLM play, zero-shot coordination, and human-AI tests. Recurrent IPPO leads the baseline ladder, but no system solves an endgame scenario.

7.1 Setup

  • All baselines trained on the same opponent mix; each selected run continued from its saved state to 250.7 million steps.Validation checks used point margin across four maps and four opponents; final policies were selected from two best checks and the last checkpoint.Source: §7.1 · p. 6

7.2 Speed and Cost

  • At 1,024 parallel games, the simulator reached 50,416 game steps per second; every method fit the tournament’s eight-hour, one-card budget.With validation, PPO baselines reached 250 million steps in 3.6–4.3 hours, QMIX in 5.5 hours, and PQN-VDN in 6.9 hours on one RTX 5090.Source: §7.2 · p. 6

7.3 Baselines and the Season 0 Ladder

  • At 1,441 Elo, recurrent IPPO led the ladder; all six baselines ranked above the three scripted opponents.Figure 5 shows Season 0 Elo ratings on test maps 47–51 with 95% intervals.Source: Figure 5 · p. 7, §7.3 · p. 7

7.4 Scenario Results

  • None of the Big Nine solved any of the eight unseen scenarios, and every system lost every game in Scenarios 5–8.In Scenarios 2 and 5–8, 12,767 of 12,793 losses ended within two ticks; losses commonly began with the weak teammate reached first.Source: §7.4 · p. 7

7.5 How Baseline Agents Cooperated

  • Stronger teams died less and combined abilities more effectively, while kill speed and simultaneous attacks did not track Elo.Warrior aura damage prevention rose from 9.0 to 11.6 points per 100 damage taken, and useful Basic healing rose from 46% to 81% across the cited entrants; Figure 6 plots six team measures against Elo.Source: Figure 6 · p. 7, §7.5 · p. 7

7.6 An LLM Team

  • Qwen3.5-9B produced 99.97% legal replies but won none of 90 games against the Big Nine and formed few coordinated attacks.It averaged 1.1 ticks per game with two or more agents dealing damage, versus opponents’ 45.7.Source: §7.6 · p. 8

7.7 Zero-Shot Coordination

  • Twenty-four of 25 learned strangers cost the recurrent IPPO team 0.8–7.2 points per game, and four made it lose more games than it won.The farther a stranger stood from teammates, the more points the team lost; this relationship was stronger for classes with nearby auras or heals.Source: §7.7 · p. 8

7.8 Human-AI Evaluation

  • The Expert Human beat recurrent IPPO in all three games; a mixed team won two of three but was rated a poor partnership.The expert used the same Agent POV as recurrent IPPO. In the mixed-team test, fluency, trust, and predictability were each rated 1, and workload rose from 22.5 against IPPO to 57.5 beside it.Source: §7.8 · p. 8

8 Limitations, Future Work, and Availability

The paper identifies limits in its initial LLM and human-AI evaluations and describes planned benchmark expansion. It also states the software licensing and release plans.

Limitations and Future Work

  • LLM results use one small model with greedy decoding, no thinking, and no memory, so they do not establish how larger reasoning models coordinate.The authors identify evaluation with thinking and memory as future work.Source: §8 · p. 8
  • Human-AI results cover six games and one expert who designed the game, while turn-based play allowed unlimited thinking time before each move.A full human-AI game takes about 60 minutes; the authors say these games mainly demonstrate studies the benchmark makes possible.Source: §8 · p. 8

Future Work

  • MARL-BGs currently has one mode, with additional modes, classes, abilities, maps, and scenarios planned as future expansion.The authors say support and expansion are planned for at least the next three years.Source: §8 · p. 8

Availability

  • The paper specifies Apache-2.0 licensing, preserves licenses for vendored code, and plans to release code and training checkpoints after manuscript acceptance.Baseline and tournament-entrant checkpoints are planned for Hugging Face.Source: §8 · p. 9

9 Conclusion

The conclusion presents MARL-BGs as a rich but computationally efficient benchmark for heterogeneous team competition. Its initial results show both coordinated ability use and remaining challenges in scenarios and partnerships.

Conclusion

  • 50,000 5v5 game steps per second run on one RTX 5090 with 1,024 parallel games.The conclusion describes the benchmark as rich yet cheap to run.Source: §9 · p. 9
  • The evaluation combines verified endgame scenarios, an equal-budget tournament, and 11,192 metrics, alongside six deep MARL baselines and three scripted opponents.The tools also include an LLM-agent API and human-play and replay clients.Source: §9 · p. 9
  • Initial results show strong teams combine abilities, but no system solves a scenario, learned agents partner poorly with strangers and humans, and an expert human beats the tournament winner.Source: §9 · p. 9

AI Disclosure

  • The authors state that AI assistance was used to refine grammar, clarity, and structural flow, and that the content was verified by the authors.Source: §9 · p. 9

Supplementary Material

The supplementary appendix provides supporting detail for pointers in the paper and identifies its contents for readers checking those details.

Supplementary Material

Start Here: The Website

The website provides browser-based access to MARL-BGs demonstrations, rules, results, models, and tool guides. Its pages cover watching games, learning the game, using the clients, and reproducing or extending experiments.

Website resources

  • The site has 91 browser pages, and its links to GitHub and Hugging Face are set to open upon manuscript acceptance.Resources and news pages include citation information, papers using the benchmark, questions and answers, bug reports, and updates.Source: Start Here: The Website · p. 11

Watch real games

  • The Replay Viewer supports Oracle or agent POV, tick-by-tick playback, frame explanations, and metric inspection for recorded games.Examples include Season 0’s top two systems and an Expert Human game against recurrent IPPO.Source: Start Here: The Website · p. 11

Play with the BattleClient

Learn the game

Scenarios and results

  • Scenario pages show each of eight starts and verified winning lines, while the results pages provide Season 0 tables, matchup data, and tournament rules.Source: Start Here: The Website · p. 11

Models and tools

  • The site offers model downloads, tutorials, and 47 guides covering training, evaluation, metrics, tournaments, replays, LLM agents, and experiment reproduction.The model library includes six Season 0 baselines and seven fixed recurrent MAPPO models.Source: Start Here: The Website · p. 11

S1 What Is in This Appendix

The appendix documents the benchmark comparison, game rules, engine, evaluations, baseline training, and additional experiments. It also identifies supporting evidence and source-code materials.

Appendix contents

  • Sections S2–S10 provide details on benchmark grading, Team Deathmatch rules, the engine, endgame scenarios, tournament runs, baselines, LLM evaluation, teamwork, zero-shot coordination, and human games.The appendix describes methods and setups behind several main-paper sections, including how experiments were conducted and interpreted.Source: S1 What Is in This Appendix · p. 11

Table 1 evidence

  • The appendix lists table1_evidence.csv as the cell-by-cell evidence for Table 1’s comparison of sixteen benchmarks.The file is described as an ancillary arXiv submission file that can be opened in a spreadsheet program.Source: S1 What Is in This Appendix · p. 11

Source code

  • The source code, planned for release on GitHub upon manuscript acceptance, includes the simulator, tools, six baseline learners, examples, and experiment scripts.Its README.md explains how to run it.Source: S1 What Is in This Appendix · p. 11

Table 1: How the Comparison Was Graded

Table 1 compares sixteen MARL benchmarks and games across twenty-two features. The section explains the grading method, rules for assigning marks, benchmark releases considered, and evidence for each cell.

Table 1: How the Comparison Was Graded

S2.1 Method

The grading uses each benchmark’s official releases as of September 2026 and counts only what it ships. The authors checked quoted evidence and reviewed the marks against the stated rules.

S2.1 Method

  • Each benchmark is graded using its official paper, repositories, companion repositories, and documentation as of September 2026.Dota 2 is graded using the OpenAI Five paper and the game as shipped by Valve because it has no released benchmark.Source: S2.1 Method · p. 12
  • Only features shipped by the benchmark count; third-party add-ons, re-implementations, and checkpoints are excluded, while outside documentation may describe official game behavior.Source: S2.1 Method · p. 12
  • Of 920 quoted sources, 917 were found by the fetch-and-search script; the remaining three were checked by hand, and two searches documented absent features.Every cell had a verbatim quote except the tournament-rating cells for SMAX and VMAS, whose repository searches found nothing.Source: S2.1 Method · p. 12
  • After evidence collection, each mark was reviewed against the grading rules, and a second review checked every reason against its sources.Downloads, links, and competitions were checked during grading, and the table and appendix include corrections from the second review.Source: S2.1 Method · p. 12
  • MARL-BGs’ recurring tournament and released agent population marks are committed for public release, while its working zero-shot tools need no dagger.The released agent population used by the zero-shot tools is covered by the agent-population dagger.Source: S2.1 Method · p. 12

S2.2 Rules for Each Row

This section defines the benchmark-comparison rubric and Team Deathmatch rules, class and map design, engine verification, evaluation protocols, and baseline training and compute. It also describes LLM-team prompts and evaluation, reporting analyses of its behavior, teamwork, zero-shot coordination, and Expert Human games.

S2.2 Rules for Each Row

  • Table S1 defines row-by-row ✓, ◦, and ✗ criteria, including requirements for verified scenarios, stronger scripted opponents, interaction metrics, curriculum, and zero-shot coordination.For example, a zero-shot coordination “yes” requires both mixed-team evaluation and a downloadable pool of trained partners; a “yes” for interaction metrics requires statistics for at least three interaction types.Source: S2.2 Rules for Each Row · pp. 12, 14, Table S1 · p. 12

S2.3 Releases Graded for Each Benchmark

  • The grading review uses the JaxMARL paper and repository for SMAX, and specified papers, repositories, packages, and competition materials for Gigastep and Lux S3.For Lux S3, the review also checked a competitor’s public code only to confirm that official training code or agents were absent.Source: S2.3 Releases Graded for Each Benchmark · p. 14, Table S2 · p. 15

S2.4 Evidence for Each Cell

  • The file table1_evidence.csv records quoted support for all 352 cells across 16 benchmarks, with one evidence row per quoted passage.Its fields include benchmark, Table 1 row, feature, mark, reason, source link, and verbatim source quote.Source: S2.4 Evidence for Each Cell · p. 15

S3 Team Deathmatch: Rules, Classes, and Maps

  • Team Deathmatch’s rules, classes, and maps are specified in map units on 20-by-10-unit maps; the mode is turn-based, not real-time, and has no per-turn time limit.The section says World of Warcraft battlegrounds inspired the benchmark’s name and its planned King of the Hills and Capture the Flag modes.Source: S3 Team Deathmatch: Rules, Classes,… · p. 15

S3.1 Rules

  • Agents act simultaneously in deterministic ticks, and a team wins by reaching 20 points with a lead; games draw on a tie at 20 or after 300 ticks.Combat resolves before movement, damage and healing are combined before deaths are checked, and deaths score one point—or two when the agent starts the tick in its team’s Red Zone.Source: S3.1 Rules · p. 16

S3.2 Classes

  • Each class has a Basic, passive, and Ultimate with a 30-tick cooldown; the described Mage amplifies damage, while the Warrior protects allies and can stun and slow an enemy.The Mage has the strongest Basic and lowest health; the Warrior has the most health, a weak Basic, and a charge that passes over obstacles.Source: S3.2 Classes · p. 17

S3.2 Classes; S3.3 Maps

  • Distinct class roles include the Hunter’s longest stun, the Rogue’s highest base speed, and the Priest’s exclusive healing; the 52 maps are split across curriculum, training, validation, and test.The built-in curriculum uses maps 0–11 and grows teams from 1v1 to 5v5; researchers can define stages mixing team sizes, maps, and winning scores.Source: S3.2 Classes · p. 17, S3.3 Maps · p. 18

S4 Engine, API, and Testing

  • The JAX engine uses fixed-shape state, pure functions, and in-place game restarts; 9,583 Python tests and cross-component checks cover rules, fairness, information limits, and saved files.Hosted CI runs Python tests in 19 parallel shards alongside formatting, lint, type, and client checks on every pull request and main-branch push.Source: S4 Engine, API, and Testing · p. 21, S4.1 Engine · p. 21, S4.2 Tests · p. 21

S4.5 Repeatability

  • All 7,200 games in two deterministic-GPU round robins matched, and recording replays or changing metrics settings did not change outcomes.The runs used nine entrants, 200 games per pairing, 128 games in parallel, and one RTX 5090, with no measurable time cost for deterministic mode.Source: S4.5 Repeatability · p. 22

S5.1 Endgame Scenarios

  • The eight endgame scenarios load exact in-progress snapshots and provide nine verified winning lines; Season 0 tested every Big Nine member across all scenarios.Scenario 1 has two winning lines, each three ticks long; each other scenario has one. Season 0 ran 20,480 games in 297 seconds on one RTX 5090, including loading and compilation.Source: S5.1 Endgame Scenarios · p. 23

S5.2 Tournament Rules; S5.3 Tournament Seeds

  • The tournament specifies monthly submissions, audited training, and a shared opponent pool; paired games exchange spawn ends, and published seeds support reproducibility.Season 0 used 3,600 seed numbers for 7,200 games. From Season 1, challenger root seeds are drawn at play time, published with results, and kept separate from training seeds.Source: S5.2 Tournament Rules · p. 23, S5.3 Tournament Seeds · pp. 24–25

S5.4 Full Metrics for a Whole Field

  • Full metrics for all 7,200 Season 0 games took 834 seconds and 392 MB, versus 488 seconds and 40 MB with priority metrics only.The analytical Replay Viewer searches all 11,192 metric columns; both runs used one RTX 5090 with 128 games in parallel, and all games repeated exactly.Source: S5.4 Full Metrics for a Whole Field · p. 25

S6 Training the Baselines

  • Baseline training combines shaped rewards, mixed self-play and scripted opponents, staged validation, and hyperparameter search with continuations to 250,675,200 game steps.Search tested 84 runs across two studies; reward scaling by 10 passed for both Q methods, while no PPO change passed. Validation selected checkpoints by point margin against a panel of four opponents.Source: S6.1 Reward · p. 25, S6.2 Opponents · p. 26, S6.3 Validation and Checkpoint Selection · p. 26

S6.5 Compute

  • 29,878 game steps per second is the reported recurrent MAPPO training speed; it used 5.0 GB peak JAX memory and 4.8 GB peak RAM, while baseline training took 101.6 GPU-hours.The training-speed measurement used 1,024 games by 32 ticks in pure self-play. The 101.6 GPU-hours covered the search studies, feedforward MAPPO reward run, and six continuations.Source: S6.5 Compute · pp. 27–28

S7.1 Setup

  • The LLM API used defaults except for a fallback that allowed play to continue after a bad reply, and the team included no earlier turns in its prompts.Researchers can customize prompts, request and reply formats, thinking, sampling, reply length, and prompt history; the agent function can run through a provider API or locally while retaining the text game view and legality check.Source: S7.1 Setup · p. 28, Table S11 · p. 28

S7.2 The Prompt

  • Each LLM prompt combined rules and abilities, map obstacles, the actor’s permitted view, prior observed actions, legal choices, and reply instructions.The Big Nine prompts averaged 4,038 tokens; the example full prompt was 14,303 characters in 101 lines.Source: S7.2 The Prompt · p. 28

S7.3 Results Against Each Member of the Big Nine

  • 99.97% of the Qwen3.5-9B team’s replies were legal; 62,629 calls averaged 1.67 seconds at the median, and all 90 Big Nine games took 3.5 hours.In the scenarios, 9,610 calls averaged 3,011 input tokens and 12.2 output tokens; 2,048 games took 22 minutes, with a 19.9-second median call wait.Source: S7.3 Results Against Each Member of… · p. 30, Table S12 · p. 31

S7.4 Teamwork Compared With Its Opponents

  • Against the Big Nine, 94.7% of the LLM team’s legal replies chose no attack, and 98.8% of its moves went east or north; scenario replies chose no attack 84.8% of the time.Within the Big Nine games, 61.8% of moves went east and 37.0% went north.Source: S7.4 Teamwork Compared With Its… · p. 31, Table S13 · p. 31

S8 How Agents Cooperate

  • Season 0 teamwork analysis replayed 7,200 scheduled games and tested Spearman correlations between 145 team-level metrics and Elo across nine entrants.The analysis used exact permutation p-values and Holm and Westfall-Young max-statistic corrections for metrics that varied.Source: S8 How Agents Cooperate · p. 31, Table S14 · p. 32

S9 Zero-Shot Coordination

  • Across 45 learned-stranger changes against individual opponents, 44 were below zero; stranger fit tracked how far agents strayed from their class’s home spacing.Recurrent MAPPO fit best in every class except Priest, while PQN-VDN—second in Season 0 Elo—tied for the largest cost. Stranger spacing changes were 0.08 map units closer for recurrent MAPPO, 0.02 farther for QMIX, 0.30 for feedforward IPPO, 0.58 for feedforward MAPPO, and 1.37 for PQN-VDN.Source: S9 Zero-Shot Coordination · pp. 32–33

S10 The Expert Human’s Games

  • The Expert Human played six turn-based games under tournament rules, both controlling all five Team A agents against recurrent IPPO and controlling the Mage alongside it against PQN-VDN.The analysis compared the three full-team games with recurrent IPPO’s own play, tested Ultimate timing against randomized timing, and examined available actions from tick-by-tick replays.Source: S10 The Expert Human’s Games · pp. 33–34, Table S16 · p. 34
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