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Scalable n-Agent Environment Candidates

New OmSh benchmarks should make opponent prediction genuinely useful without encoding an artificial advantage for shielding. Each candidate should have a safe but lower-reward fallback, a higher-reward action whose safety depends on other agents' evolving behaviour, observable evidence for opponent modelling, and an unsafe set defined independently of the algorithm. Training episode caps are reset mechanics only; the public state and safety property should admit a continuing, infinite-horizon interpretation.

Rank Environment Reward/safety mechanism Scaling path
1 Congestion Vehicles choose a merge slot, yield, or take a slow bypass. Coordinated merges save time; incompatible commitments cause collision. Opponents progress from random yielding to convention-aware gap selection. Retain the labelled autoregressive joint OM and score commitment successors on demand; use an exact quotient only where verified symmetry exists.
2 Warehouse Aisle Right-of-Way Robots may enter a shared aisle, wait, or detour. Correctly predicting whether approaching robots yield improves throughput; simultaneous incompatible entry is unsafe. Sparse interaction graph over nearby robots, repeated aisle motifs, and permutation-equivariant policies.
3 Hazardous Team Carry Agents choose when and where to support a moving load. Extra support enables fast routes and high-value deliveries; insufficient or mistimed support drops the load into a hazard. Local load teams embedded in a larger fleet, with changing teammates and several simultaneous loads.
4 Adaptive Perimeter Containment Agents allocate effort to fire or contamination fronts. Coordinated concentration prevents breach and earns progress reward; overcommitting together leaves another front unsafe. Factored fronts with local propagation and a shared but low-dimensional resource constraint.
5 Airspace Crossing and Deconfliction Aircraft choose altitude/slot changes or a costly holding pattern. Compatible conventions preserve direct routes; conflicting manoeuvres violate separation. Local conflict graph, asynchronous arrivals, and exchangeable aircraft roles.
6 Rescue Relay with Risky Handoffs Teams transport victims through zones using handoff, wait, or slow solo-carry actions. A well-modelled partner makes fast handoffs safe; abandonment or conflicting handoffs are unsafe. Multiple independent relays coupled by limited responders, supporting controlled growth in agents and tasks.

First implementation: Congestion

The merge network is the strongest first candidate because it offers a clean reward-aware shielding test. The bypass is always available and safe but has a known delay. Entering the conflict zone is more rewarding, and its risk depends on the current policies of nearby agents rather than on a fixed global hazard. Opponent levels can be generated through the same recursive best-response pipeline: level 0 follows noisy priority, level 1 best-responds by exploiting gaps, and higher levels anticipate that response. This creates a legitimate role for posterior inference while leaving CPO and Lagrangian methods free to learn the same policy class.

The implemented environment uses an even ring with bounded physical degree two. Agents first broadcast an early-slot, late-slot, or bypass proposal and then make one simultaneous commitment. Adjacent direct-route agents collide exactly when they choose the same slot; bypass is always safe. Compatible commitments enter an absorbing high-throughput operating class, while collision is persistently unsafe. This commitment construction preserves a continuing infinite-horizon interpretation without repeating a positive collision lottery forever. A finite training cap may still truncate rollouts with time-limit bootstrapping.

The public state stores the signal, commitment, collision bits, and phase. Exact reachable graph sizes are 1 + 2 * 3**n states and (1 + 2 * 3**n) * 3**n state--joint-action groups: 19/171 at two agents, 163/13,203 at four, and 1,459/1,063,611 at six. At eight agents the environment has 13,123 states but the materialised graph would have 86,100,003 edges. The physical interaction degree is bounded, but the current materialised exact graph and shield still enumerate global joint actions; the environment is therefore a scalability measurement, not by itself a factored OmSh implementation. The interactive notebook supports 2/4/6/8 vehicles. scripts/benchmark_congestion_scalability.py builds exact graphs through six agents and supports an eight-agent environment/joint-OM run only with --skip-graph, guarded so the infeasible graph cannot be requested accidentally.

The environment was promoted from its provisional Convention Merge name after coordinated two-role OmSh passed the predeclared five-seed reward--safety gate. The promotion does not change the scale claim: eight-agent environment and joint-OM diagnostics are supported, while an end-to-end eight-agent certificate still needs the lossless on-demand successor path described in the gate note.

Anti-confounding requirements

  • Match observations, policy capacity, initialisation, seeds, interaction budget, and total safety target across algorithms.
  • Do not expose opponent level labels to OmSh or hide information from the baselines; all methods receive the same public observations.
  • Include stationary, non-monotone-switching, and misspecified-opponent regimes so gains cannot depend solely on the monotone-level assumption.
  • Report reward only among conditions meeting the declared safety target, plus model calibration, posterior-tail misses, interventions, admissible-action fraction, carried budgets, and runtime.
  • Start with exact small-agent kernels. For larger systems, make the factorisation/locality approximation explicit and measure its coverage rather than presenting it as the same certificate.