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Environment Objective And Atom Conventions

Temporal-game environments should define one SpecPair for every exposed env.possible_agents entry. Cooperative tasks may still use related formulas, but each learning agent should have an explicit monitor so NashConv, AlphaRank, counterfactual replay, and plots all operate on the same agent set.

Nash equilibrium is an experiment-level property of the learned policy profile, not a trajectory atom. Environment labels and SpecPair.formula_str values must not contain NashConv, AlphaRank, equilibrium, verifier, or policy-profile signals. Those checks happen after training: NashConv estimates whether a unilateral deviation improves objective satisfaction under the existing success-threshold path.

Preferred atom style:

  • use domain events, not generic implementation signals
  • prefer apple_collected over reward
  • prefer food_metabolized over food_reward
  • prefer resource_claimed over resource_reward
  • use player_i_* atoms when a formula is meant to credit only one learner
  • keep aggregate atoms only when the formula intentionally reasons about team state

The current per-environment intent is:

  • Coins uses the agent-specific own-coin-first formula (!player_i_mismatched_coin_collected) U player_i_matched_coin_collected. Partner harm is an event label and shaped-reward signal, not an equilibrium atom.
  • Pursuit Evasion keeps asymmetric guard/intruder objectives and now uses semantic collision atoms such as guard_intruder_collision.
  • Chemistry gives every learner an individual food-then-XY objective over player_i_food_metabolized_ever and player_i_xy_metabolized; the easier chemistry sanity objective is the individual food-only formula F player_i_food_metabolized. Treat food-only as a rational-synthesis smoke test rather than a strong temporal/strategic benchmark. The intermediate chemistry objective is F (player_i_food_metabolized_ever & xy_metabolized), which requires individual food setup plus a shared XY milestone.
  • Harvest gives every learner an individual harvest or safe-harvest objective over player_i_apple_collected and player_i_zapped.
  • Territory gives every learner an individual claim objective over player_i_resource_claimed, with all_zappers_ready retained as a shared peacefulness condition.
  • Gift Refinements gives every learner an individual refined-then-consume objective over player_i_refined_gift_received_ever and player_i_tokens_consumed; the easier Gift Refinements smoke objective is F player_i_tokens_consumed. Do not replace it with aggregate F tokens_consumed unless the experiment is explicitly team-level.