The Convention Trap: Why a 24-Point Teammate Scores 2 With a Stranger

In two-player Hanabi, the Simplified Action Decoder scores 23.97 out of a possible 25 when it plays alongside a copy of itself. Change one thing, the random seed used to train the partner, so that both agents come from the same algorithm, the same hyperparameters and the same codebase, and the pair scores 2.52 (Hu et al., 2020, "Other-Play" for Zero-Shot Coordination, arXiv:2003.02979). Neither agent got worse. They simply never agreed on what a hint means.

That single pair of numbers reframed a decade of cooperative multi-agent reinforcement learning. Self-play, the technique that produced superhuman Go, poker and StarCraft, turns out to measure two things at once in cooperative settings: how well an agent plays, and how thoroughly it has memorised a private language that only its own copies speak. The second component can be almost all of the score. The research programme that followed, zero-shot coordination, is essentially an effort to separate them, and the separation matters now for a reason the original authors did not have in view: production systems are increasingly built from agents that were trained separately and must cooperate on first contact.

Why this matters: Any evaluation that pairs a policy with itself conflates competence with convention. If you are building systems where independently trained agents, third-party agents, or humans must coordinate without a pre-agreed protocol, the self-play number tells you almost nothing about what will happen, and the gap between self-play and cross-play is the only honest measure you have.

TL;DR

• A state-of-the-art Hanabi agent drops from 23.97 to 2.52 when paired with an independently seeded copy of itself. The gap is the part of the score that was arbitrary convention.
• Cooperative tasks have symmetries, that is, relabellings of actions that leave the payoff structure identical. Self-play is free to break those symmetries any way it likes, and two runs break them differently.
• Other-play fixes this by optimising expected return under a randomly relabelled partner, lifting cross-play from 2.52 to 15.32, and to 22.07 with an auxiliary task, while leaving self-play essentially unchanged at about 24.
• Off-belief learning removes conventions by construction rather than by penalty, reaching 24.10 self-play and 23.76 cross-play with itself at iteration level 4.
• Convention-free agents give up real capability. Human Hanabi pairs communicate about +26.2 points worth of meaning beyond a hint's literal content; AI-AI pairs measure about -0.7 (Fukushima et al., 2026, arXiv:2609.11489).
• People do not reward this progress the way the benchmark does. In a single-blind study, humans scored no better with an other-play agent than with a hand-coded bot and preferred the bot on nearly every subjective measure (Siu et al., 2021, arXiv:2107.07630).
• Not every cross-play gap is a convention problem. In Overcooked, most of it turned out to be poor state coverage, which means the diagnosis has to come before the fix (Gessler et al., 2025, arXiv:2503.17821).

At a Glance

flowchart LR
    T["Cooperative task with symmetries"] --> SP[Self-play training]
    SP --> P1["Policy, seed A"]
    SP --> P2["Policy, seed B"]
    P1 --> M1["Paired with own copy: 23.97"]
    P1 --> M2["Paired with seed B: 2.52"]
    M2 --> D[Gap equals private convention]
    D --> F[Other-play and off-belief learning]
    F --> M3["Cross-play: 22 to 24"]

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    class SP,P1,P2 purple
    class M1 teal
    class M2,D rose
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[IMAGE: Two side-by-side score dials, one reading 23.97 labelled "with my own copy" and one reading 2.52 labelled "with an identically trained stranger", with a bracket between them annotated "private convention". Caption: "The same policy, the same algorithm, two seeds. The bracket is what self-play evaluation hides."]

Before Anyone Measured Cross-Play

The intellectual groundwork is older than deep RL. David Lewis argued in Convention (1969) that coordination problems are solved by arbitrary regularities sustained only by mutual expectation: which side of the road to drive on is not a fact about roads. Multi-agent planning formalised the difficulty two decades later. Bernstein, Givan, Immerman and Zilberstein proved that optimal finite-horizon decentralised control, the Dec-POMDP, is complete for nondeterministic exponential time for as few as two agents, which is two complexity classes above the single-agent partially observable case (Bernstein et al., 2002, Mathematics of Operations Research 27(4)). The hardness is not in the size of the action space. It is in the fact that each agent conditions on a private observation history, so no agent can evaluate its own policy without knowing which policy the other happens to run.

Stone, Kaminka, Kraus and Rosenschein named the practical version of this in 2010: ad hoc autonomous agent teams, where an agent must cooperate with teammates it has never met and cannot negotiate with in advance (Stone et al., 2010, AAAI). The paper was a call for theory and benchmarks, and for most of a decade the field answered it with environments that measured self-play.

Then two benchmarks arrived in the same year and made the omission visible. The Hanabi Challenge proposed the cooperative card game as a frontier problem and, crucially, defined two challenges rather than one: self-play, where a single joint policy is learned, and ad hoc play, where an agent is dropped in with a held-out pool of partners after a handful of observation games (Bard et al., 2020, Artificial Intelligence 280, arXiv:1902.00506). The paper's own framing is blunt about why: a policy that scores highly in self-play is of little use if teammates must follow it exactly. In parallel, an Overcooked-based environment showed the same asymmetry with human partners: self-play and population-based agents performed very well with themselves and significantly worse than human-aware agents when paired with a learned model of human play, a pattern that reproduced, more weakly, with real people (Carroll et al., 2019, NeurIPS, arXiv:1910.05789).

timeline
    title From conventions to cross-play
    1969 : Lewis argues conventions are arbitrary regularities sustained by expectation
    2002 : Bernstein et al. prove finite-horizon Dec-POMDP is NEXP-complete
    2010 : Stone et al. define ad hoc autonomous agent teams
    2017 : Leibo et al. introduce sequential social dilemmas for mixed motives
    2019 : Carroll et al. show self-play agents underperform with human partners in Overcooked
         : Hu and Foerster set self-play state of the art in Hanabi with the Simplified Action Decoder
    2020 : Bard et al. publish the Hanabi Challenge with a separate ad hoc play task
         : Hu et al. introduce other-play and report cross-play of 2.52 for plain self-play
    2021 : Hu et al. remove conventions by construction with off-belief learning
         : Siu et al. find humans prefer a rule-based Hanabi bot to a learned one
         : Leibo et al. release Melting Pot with over eighty held-out co-player scenarios
    2022 : Meta's CICERO reaches human-level Diplomacy with language and a human behaviour model
    2025 : Gessler et al. show most Overcooked cross-play failure is state coverage, not convention
    2026 : Fukushima et al. quantify the implicit-communication gap between human and AI pairs

How Self-Play Manufactures a Private Language

Symmetries and equivalence classes of policies

Start with the structure that makes the problem possible. A cooperative task often admits a group \(\Phi\) of transformations that relabel actions and observations while leaving the transition and reward functions invariant. In Hanabi, the identity of a colour is such a relabelling: swap "red" and "blue" everywhere, in the deck, in the hints and in the agents' policies, and you have an identical game. Formally, for \(\phi \in \Phi\) and joint policy \(\pi = (\pi^1, \pi^2)\),

where \(J\) is expected return. The joint relabelling is free. Relabelling only one side is not.

That asymmetry is the trap. Self-play maximises \(J(\pi, \pi)\) over a single policy, which means it optimises within one equivalence class and never has a reason to prefer one class over another. Gradient descent takes whichever class the initialisation and the seed steer it into. The result is a policy whose behaviour encodes a specific, arbitrary assignment of meaning, and whose partner must share that assignment exactly.

[IMAGE: Diagram of policy space divided into nine shaded equivalence classes of equal value plus one smaller distinct region, with two training trajectories starting from different initialisations and terminating in different classes, each annotated "self-play optimum, J equals 1.0". Caption: "Self-play has no preference between equivalent classes, so the seed chooses."]

The zero-shot coordination objective

Zero-shot coordination states the problem as a different optimisation. Given an algorithm that produces policies, the objective is expected return when two agents are drawn independently from the algorithm's output distribution:

Note that this is a property of the algorithm, not of a policy, which is what makes it a hard target. You cannot evaluate a single trained network against this objective; you must train several and pair them. The empirical estimator is cross-play: train \(k\) policies on \(k\) seeds, evaluate all \(k(k-1)\) ordered pairs, and average. Self-play is the diagonal of that matrix and cross-play is everything off it.

[IMAGE: A 5-by-5 heatmap of pairwise Hanabi scores for five independently seeded agents, diagonal cells dark green near 24, off-diagonal cells dark red near 2, with a second panel showing the same matrix for other-play agents where off-diagonal cells are green near 22. Caption: "Self-play is the diagonal. Cross-play is the rest of the matrix, and it is where coordination actually lives."]

Other-play: make the arbitrary unprofitable

If the problem is that conventions are free, the fix is to charge for them. Other-play optimises the expected return when the partner's policy has been transformed by a uniformly drawn element of the symmetry group:

A strategy whose payoff depends on a particular labelling now loses in expectation, because the labelling is resampled every episode. What survives is behaviour that is invariant under the group, or that depends only on features the group does not permute. In the lever game below, that is the single lever with a unique payoff; in Hanabi, it is strategies grounded in the game's own structure rather than in an agreed code.

The cost is representational. Other-play restricts the policy class to the equivariant ones, and if the optimal policy genuinely requires symmetry-breaking, that optimum is now unreachable. The remarkable empirical finding is how small the cost is in Hanabi: self-play falls from 23.97 to 23.93 while cross-play rises from 2.52 to 15.32 (Hu et al., 2020). The private convention was buying almost nothing in return for everything it cost.

Off-belief learning: remove the channel, not the incentive

Other-play still permits conventions that happen to be symmetry-invariant, and it requires the designer to specify \(\Phi\). Off-belief learning takes a different route. An agent is trained to act optimally under the counterfactual assumption that its partner has been playing a fixed, known, convention-free baseline policy \(\pi_0\) up to the present moment, and will play the learned policy from here on. Beliefs over hidden state are computed with respect to \(\pi_0\), so a partner's past action carries exactly the information \(\pi_0\) would have put in it and no more. No secret meaning can accumulate, because the belief update refuses to read any.

Iterating the construction gives a hierarchy: level 1 grounds against a random baseline, level 2 grounds against the level-1 policy, and so on, each level able to rely on the previous level's now-public behaviour. At level 4, the result is 24.10 in self-play and 23.76 in cross-play with itself (Hu et al., 2021, Off-Belief Learning, ICML). The paper also reports what happens when you mix families: an OBL level-4 agent paired with an other-play agent scores 14.46, well below either agent's own cross-play. Convention-freedom is not a universal protocol. It is one more thing two agents have to share.

stateDiagram-v2
    [*] --> L0
    L0: Level 0 baseline, uniform random
    L1: Level 1, grounded on random partner
    L2: Level 2, grounded on level 1
    L3: Level 3, grounded on level 2
    L4: Level 4, self-play 24.10
    L0 --> L1: train against fixed beliefs
    L1 --> L2: freeze and re-ground
    L2 --> L3: freeze and re-ground
    L3 --> L4: freeze and re-ground
    L4 --> [*]: cross-play 23.76 with itself

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    classDef emerald fill:#047857,stroke:#34d399,stroke-width:1px,color:#fff
    class L0 slate
    class L1,L2,L3 purple
    class L4 emerald

Why the self-play score barely moves

The single most useful fact in this literature is that removing conventions costs almost nothing in self-play. SAD at 23.97, SAD with other-play at 23.93, OBL level 4 at 24.10: within noise of each other. If conventions were carrying real information, constraining them would hurt. They were not; they were carrying coordination that the agents could have obtained from the game's public structure instead. The private language was a local optimum that self-play had no pressure to leave.

Seeing It in Motion

The two training loops differ in one place, and that place determines everything downstream.

flowchart TB
    subgraph SP["Self-play loop"]
        A1[Sample episode] --> A2[Partner equals own policy]
        A2 --> A3[Update toward joint return]
        A3 --> A1
    end
    subgraph OP["Other-play loop"]
        B1[Sample episode] --> B2["Draw relabelling from symmetry group"]
        B2 --> B3[Partner equals relabelled policy]
        B3 --> B4[Update toward expected return]
        B4 --> B1
    end
    SP --> R1["Convention is free, cross-play 2.52"]
    OP --> R2["Convention costs return, cross-play 15.32"]

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The failure at play time is a chain of three steps, and it is worth watching the mismatch propagate rather than treating it as a single event.

sequenceDiagram
    participant A as Agent A, seed 1
    participant G as Game state
    participant B as Agent B, seed 2
    A->>G: Hint colour red to partner
    Note over A: Convention: colour hint means play it now
    G->>B: Observes hint colour red
    Note over B: Convention: colour hint means it is safe to discard
    B->>G: Discards the hinted card
    G->>A: Card lost, firework blocked
    Note over A,B: Both acted optimally under their own code
    A->>G: Hint rank to force a play
    G->>B: Reads rank hint as a discard signal
    B->>G: Discards again, life token lost

Nothing in that trace is a bug, and no agent made a mistake relative to its own training. The interpretive step between them is the only broken component, and it is the one no self-play metric observes.

Watch It Run

By the Numbers

Two-player Hanabi, maximum score 25. All figures are averages over many games with the paper's own standard errors.

Implicit communication, measured as the gap between the failure probability predicted from a hint's literal content and the failure rate actually observed, over roughly 101,000 replayed Hanabi play actions:

Sources: other-play and the Hanabi tables from Hu et al., 2020, arXiv:2003.02979; OBL figures from the ICML 2021 version of Hu et al., 2021 (the arXiv and ICML versions of that table disagree on one rule-based-partner cell, 16.00 against 16.76, so treat that single figure as uncertain); convention-gap figures from Fukushima et al., 2026, arXiv:2609.11489, whose exact values depend on their estimator and should be read as a measured contrast between pairings rather than absolute constants.

[IMAGE: Horizontal bar chart of cross-play scores for the seven Hanabi configurations in the table, bars ordered ascending from SAD at 2.52 to OBL level 4 at 23.76, with a vertical dashed line at the self-play level of roughly 24 and each bar annotated with its self-play score where available. Caption: "Self-play scores are flat across the whole family. Cross-play spans an order of magnitude."]

A Concrete Example

Work the lever game through, because the arithmetic is the entire mechanism in miniature (Hu et al., 2020).

Setup. Two players independently choose one of ten levers. If both choose the same lever, each receives that lever's payoff; otherwise both receive zero. Nine levers pay 1.0. One lever pays 0.9.

Step 1: what self-play learns. Self-play maximises \(J(\pi, \pi)\). Any of the nine high-payoff levers gives \(J = 1.0\), the 0.9 lever gives \(J = 0.9\), so the optimiser picks one of the nine. Which one depends on the seed. Training return reaches 1.0 and the learning curve looks perfect.

Step 2: pair two independently trained self-play agents. Each has committed to one of nine indistinguishable levers. The probability they chose the same one is \(1/9\), and the expected return is

Random uniform choice over all ten levers scores \(\tfrac{1}{10} \times \overline{\text{payoff}} \approx 0.1\). The trained agent beats random guessing by about 0.011, having reached a perfect training score.

Step 3: what other-play does. Under a relabelling drawn uniformly from the permutations of the nine identical levers, no particular high-payoff lever is identifiable. Expected return for any policy that selects "a 1.0 lever" stays at \(1/9\). The 0.9 lever is fixed by every element of the group because its payoff is unique, so a policy selecting it earns

Other-play therefore converges on the strictly worse lever, and that is the right answer. It gives up 10% of the achievable payoff to gain a factor of eight in realised return.

Step 4: why Hanabi collapses to 2.52 rather than degrading gently. Now compose. Suppose a policy's behaviour depends on \(k\) independent arbitrary choices, each among \(m\) equally good options: which colour means "play immediately", which rank means "discard", whether a hint to the newest card means something different, and so on. Two independently trained agents agree on all of them with probability \(m^{-k}\). With \(m = 2\) and \(k = 5\), that is \(1/32\). Hanabi's hint space is far richer than a single lever, and a Hanabi score is not linear in agreement: one misread hint discards a card that a firework needed, which caps the achievable score for the rest of the episode, and three misreads end the game. The 2.52 is not a proportional degradation of 23.97. It is what happens when a composed code fails at its first symbol and the game punishes early errors permanently.

Step 5: sanity-check against the measured middle. The table above gives a useful intermediate case. Cross-play among seed-only variants of a plain self-play model scores about 20.99, much higher than SAD's 2.52. The difference is that SAD's training mechanism, which exposes a teammate's greedy action during training, makes richer private conventions learnable, and richer conventions are more fragile. Capability and brittleness came from the same place.

Where It Breaks

The symmetry group must be handed to you

Other-play needs \(\Phi\) specified. In Hanabi, colour permutation is exact and known. In a warehouse, a trading venue or a codebase, the symmetries are approximate at best and often unknown, and optimising for a misstated invariance buys robustness to transformations that never occur while leaving the real ones untouched. There is no general procedure for discovering a task's symmetry group from data.

A cross-play gap is not self-diagnosing

The Overcooked re-examination is the cautionary case. Coordination failure there is driven largely by poor state coverage: an unfamiliar partner steers the game into states the agent never saw in training, so the policy is out of distribution rather than speaking the wrong language. The authors conclude that the original Overcooked is not a suitable zero-shot coordination benchmark, and build OvercookedV2 with asymmetric information and stochasticity to make the coordination challenge real (Gessler et al., 2025, ICLR, arXiv:2503.17821). They also show that exhaustive state coverage alone is not sufficient, which rules out the lazy inverse diagnosis too.

Convention-freedom destroys something valuable

This is the deepest problem, and the 2026 measurement makes it concrete. Human Hanabi pairs rely heavily on meaning that a hint's literal content does not contain, and the convention gap quantifies it at about +26.2 points for human-human play against about -0.7 for AI-AI play, concentrated on cards that received no hint at all (Fukushima et al., 2026, arXiv:2609.11489). An agent that cannot form conventions cannot participate in the thing that makes human teams good, and the same study finds that OBL's gap rises from about +1.6 at the convention-free level to about +21.7 at a higher level, so the ladder is partly a ladder back toward implicit communication under control.

[IMAGE: Grouped bar chart of the convention gap in points for four pairings, human-human at +26.2, human-AI at +16.4, AI-AI at -0.7, and OBL at its convention-free level at +1.6, with a dashed zero line and a note that the gap is concentrated on unhinted cards. Caption: "Implicit communication is what human teams run on, and it is the thing convention removal deletes."]

Humans rate it differently than the benchmark does

Siu and colleagues ran a single-blind study pairing people with an other-play agent and with the hand-coded SmartBot. Game scores showed no statistically significant difference. Subjective ratings were lopsided: participants preferred the rule-based bot on nearly every measure, including perceived teamwork, interpretability and trust, and viewed the learned agent negatively (Siu et al., 2021, NeurIPS, arXiv:2107.07630). The authors note their own hypothesis, that learned agents would be preferred, was not supported. If the goal is a teammate people will accept, cross-play score is necessary and not sufficient.

Cross-play itself can be gamed

Maximising \(J_{\text{ZSC}}\) rewards blandness. A policy that makes no commitments, takes safe low-variance actions and signals nothing will cross-play adequately with anything, including other bland policies, while being a poor partner in absolute terms. Reporting cross-play alone invites that degenerate solution, which is why the self-play and cross-play numbers have to be read together: the interesting claim is a high cross-play score at unchanged self-play, as in the 23.93 and 15.32 pairing.

Within-algorithm cross-play is the easy version

Pairing seeds of one algorithm holds architecture, objective, hyperparameters and training environment fixed, and varies only the symmetry-breaking. Pairing different algorithms varies everything, and the scores drop accordingly: OBL level 4 with an other-play partner manages 14.46 rather than its 23.76 with its own family. Any system composed from independently developed agents is in the harder regime, and the published cross-play numbers overstate what it will get.

The underlying problem is still NEXP-complete

None of this escapes the complexity result. Zero-shot coordination methods are heuristics that restrict the policy class or the belief update so that the search becomes tractable and the solution becomes partner-independent. They provide no guarantee of optimality, and the policies they find are, by construction, not the optimal joint policy for the Dec-POMDP.

Alternative Designs

[IMAGE: Decision tree for choosing a method, branching first on whether the deployed partner is the same checkpoint, then on whether the task's symmetries are known exactly, then on whether human data exists, with the seven designs from the table as leaves. Caption: "The method follows from who the partner is, not from which paper is newest."]

Population-based training deserves a specific caution. It is the standard answer to brittleness and it does not solve this problem, because a league trained from one lineage can share a convention throughout. Diversity of strategy is not diversity of code.

How It Is Used in Practice

The clearest production-scale instance of language-mediated coordination is CICERO, which reached human-level play in Diplomacy by combining a planning engine with a dialogue model and an explicit model of human behaviour. Across more than 40 anonymous online games it scored more than double the human average and placed in the top 10% of players with more than one game (Bakhtin et al., 2022, Human-level play in the game of Diplomacy by combining language models with strategic reasoning, Science). The design lesson is that it did not try to be convention-free. It learned human conventions from human data and negotiated the rest in words.

Hanabi research has kept moving toward generality rather than peak score. R3D2 reframes the game in text and uses a distributed MARL algorithm that tolerates changing observation and action spaces, which lets a single agent play all player-count settings at once and transfer strategies between them; the authors report that it collaborates with different algorithmic agents that cannot themselves do so (Sudhakar et al., 2025, A Generalist Hanabi Agent, ICLR, arXiv:2503.14555). Melting Pot, meanwhile, became the standard way to evaluate social generalisation, pairing each substrate with held-out background populations across more than 80 scenarios so that a focal agent is always scored against co-players it never trained with (Leibo et al., 2021, ICML, arXiv:2107.06857).

The current reason to care is compositional. Systems built from language-model agents routinely pair components trained and tuned separately, and benchmarks for that setting have adopted the self-play minus cross-play gap as the measure of ad hoc teaming. An early evaluation of LLM agents on Overcooked-AI and Hanabi with unseen partners reported that they beat behaviour-cloning and PPO baselines in Overcooked and matched or beat a zero-shot-coordination baseline on most layouts, with Off-Belief Learning agents used as the Hanabi partners (Agashe et al., 2023, LLM-Coordination, arXiv:2310.03903). That is a promising signal and not a settled result: the partner pools are small and the comparison to RL baselines is sensitive to how each is tuned.

Operationally, the practice worth adopting is narrow and cheap. Train at least three seeds, publish the full pairing matrix rather than the diagonal, and treat the self-play minus cross-play difference as a first-class metric alongside the headline score. Evaluation protocol work in cooperative MARL recommends on the order of ten independent training runs and 32 evaluation episodes per interval, against a field where five seeds was the common practice (Gorsane et al., 2022, NeurIPS, arXiv:2209.10485). The matrix is a strictly larger ask than that, and in this setting it is the only measurement that distinguishes a teammate from a clone.

[IMAGE: Flow diagram of a recommended evaluation protocol: train N seeds, build the N-by-N pairing matrix, report diagonal mean, off-diagonal mean, and their difference, with a branch for cross-family pairings against a held-out algorithm. Caption: "Publishing the diagonal is reporting one number from a matrix you already computed."]

Insights Worth Remembering

1. A self-play score is a sum of two quantities with no label on either. Competence transfers to new partners; convention does not. Hanabi's 23.97 was roughly 2.5 points of the first and 21 points of the second, and nothing in the training curve distinguished them.

2. Removing conventions cost almost nothing. SAD 23.97, SAD with other-play 23.93, OBL level 4 24.10. The private language was not buying capability; it was a local optimum that self-play had no pressure to leave. That is the strongest practical argument for building convention-robustness in from the start.

3. Cross-play is a property of an algorithm, not of a checkpoint. You cannot measure it on one trained model. This is why it was missing from the field for a decade: it requires paying for extra training runs that produce no better headline number.

4. Composed conventions fail multiplicatively. Agreement on \(k\) independent arbitrary choices among \(m\) options each has probability \(m^{-k}\), and in games that punish early mistakes the score does not degrade proportionally, it collapses. Brittleness grows with exactly the mechanisms that make an agent sophisticated.

5. Convention-freedom and convention-competence are different goals. Human teams get about 26 points of implicit communication out of Hanabi hints; convention-free agents get approximately zero. Grounding is the right target for coordinating with strangers and the wrong target for coordinating with people who already have a code.

6. Benchmarks and partners disagree about progress. The agent that won on cross-play lost on human preference against a hand-written bot at equal score. If a human is the partner, subjective measures of teamwork and interpretability are part of the objective, not commentary on it.

7. A low cross-play score has at least three distinct causes. Convention mismatch, state-distribution shift, and genuine capability gaps all look identical in the aggregate number. Overcooked spent years being treated as the first when it was mostly the second.

8. Population-based training is not a fix. A league grown from one lineage can share a convention throughout. Diversity of strategy within a family says nothing about agreement across families, which is where cross-family pairings like OBL with other-play fall from 23.76 to 14.46.

Open Questions

Can symmetries be discovered rather than declared? Other-play's dependence on a hand-specified group is its binding constraint, and no general method for learning a task's symmetry group from interaction has been demonstrated at the scale where it would matter. This is known to be the gap; what is not known is whether approximate or learned symmetries degrade gracefully or catastrophically.

What is the right target when the partner distribution is humans? Measured results show that convention-free agents coordinate well with strangers and are disliked by people, and that human pairs depend on implicit meaning. Whether a single policy can be grounded enough for zero-shot play and expressive enough to acquire a partner's conventions during play is open; the ad hoc teamwork and OBL-level results gesture at a middle, without establishing one.

How much of the cross-play gap in LLM-agent systems is convention at all? The published measurements use the self-play minus cross-play gap as the metric, inherited from this literature, but language-model agents share enormous amounts of pretraining, which plausibly supplies common conventions for free. Nobody has yet separated shared-pretraining agreement from task-specific convention in those numbers.

Does the convention gap predict anything downstream? The 2026 estimator is new and gives a clean contrast between human and AI pairs. Whether it predicts human preference, trust, or performance in other cooperative tasks is unmeasured, and treating it as a general-purpose coordination metric would be premature.

Is there a protocol layer that makes this moot? Explicit negotiation, as CICERO used language and as agent-interoperability protocols propose for tool and message schemas, converts an implicit coordination problem into an explicit one. It is likely that production multi-agent systems will mostly take this route, which raises the question of what the residual implicit coordination problem looks like once the explicit part is handled, and nobody has characterised that remainder.

Sources and Further Reading

1. Hu, H., Lerer, A., Peysakhovich, A., & Foerster, J. (2020). "'Other-Play' for Zero-Shot Coordination." ICML 2020, PMLR 119, 4399-4410. arXiv:2003.02979
2. Hu, H., Lerer, A., Cui, B., Pineda, L., Brown, N., & Foerster, J. (2021). "Off-Belief Learning." ICML 2021, PMLR 139. proceedings · arXiv:2103.04000
3. Hu, H., & Foerster, J. (2020). "Simplified Action Decoder for Deep Multi-Agent Reinforcement Learning." ICLR 2020. arXiv:1912.02288
4. Bard, N., Foerster, J. N., Chandar, S., Burch, N., Lanctot, M., Song, H. F., et al. (2020). "The Hanabi Challenge: A New Frontier for AI Research." Artificial Intelligence 280, 103216. arXiv:1902.00506
5. Bernstein, D. S., Givan, R., Immerman, N., & Zilberstein, S. (2002). "The Complexity of Decentralized Control of Markov Decision Processes." Mathematics of Operations Research 27(4), 819-840. publisher · preprint
6. Stone, P., Kaminka, G. A., Kraus, S., & Rosenschein, J. S. (2010). "Ad Hoc Autonomous Agent Teams: Collaboration without Pre-Coordination." AAAI 2010, 1504-1509. PDF
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