---
artifact_kind: optimizer-card
artifact_name: psro-opponent-model
version: 1.0.0
owner: Nous · agreement-search team
last_reviewed: 2026-04-25
next_review: 2026-07-25
optimizer_kind: psro
related_phase_179_tasks: [179.4.2.6, 179.7.6, 179.7.1]
---

# Optimizer Card — psro-opponent-model v1.0.0

## 1. Identity

- **Optimizer name:** psro-opponent-model
- **Algorithm family:** Policy-Space Response Oracles (Lanctot et al. 2017) —
  empirical-game best-response loop with a meta-solver and a best-response
  oracle.
- **Implementation source:**
  `libs/nous/agreement-search/src/psro-opponent-model.ts`.
- **Intended use:** agent-to-agent negotiation (§179.7.6) and competitive
  commercial negotiation (§179.7.1) where the counterparty will adapt
  strategically to whatever the platform proposes. The recommended candidate
  must survive the counterparty's best response, not just optimize
  Pareto-product against fixed utilities.

## 2. Scoring rule

- **Utility aggregation:** game-theoretic — payoff tensor `M_p[i, j]` = party
  `p`'s true utility under the deterministic proposal-arbitration simulator's
  outcome for policy pair `(σ_A^i, σ_B^j)`.
- **Meta-solver:** replicator dynamics (general-sum convergent), fictitious play
  (zero-sum provable), or uniform (sanity control).
- **Fairness metrics reported:** Nash exploitability bound, per-party
  meta-strategy distribution, candidate marginal distribution.
- **Handling of hard constraints:** filter gate runs on every candidate
  considered by every policy.
- **Handling of uncertainty:** payoff modes `posterior_mean | lcb | thompson`
  against the §179.3.2.5 utility-uncertainty model. `lcb` penalizes over-fit to
  noisy preferences.

## 3. Inputs

- **Policy parameter space:** caller-defined; default uses an
  acceptance-threshold + concession-rate parameterization.
- **Best-response oracle:** (1, λ)-evolution strategy with Gaussian
  perturbations; deterministic given seed.
- **Game simulator:** caller-supplied `simulateGame(σ_A, σ_B) → outcome`.
  Default Concordia simulator intersects accepted candidate sets, picks the
  survivor by joint policy-weighted score, and falls back to BATNA on
  no-overlap.
- **Time / iteration budget:** `psroIterations × oracleSearchBudget`.
- **Randomness:** seeded `mulberry32` for both meta-solver and oracle.

## 4. Outputs

- **Accepted candidate contract:** the most-robust candidate by marginal
  probability under `Σ π_A(σ_A) π_B(σ_B) · 1[game(σ_A, σ_B) chose c]`.
- **Per-party meta-strategy distribution:** `π_A`, `π_B`, ..., showing how the
  equilibrium mixes over policies.
- **Exploitability trace:** Σ over parties of (BR payoff − meta payoff) decaying
  toward zero as the empirical game approaches an ε-Nash equilibrium.
- **Empirical payoff tensor:** preserved for audit.

## 5. Evaluation

| Metric                          | Value                                 | Evaluator card                                                      | Date       |
| ------------------------------- | ------------------------------------- | ------------------------------------------------------------------- | ---------- |
| Exploitability decay            | decays toward 0 within 5–10 PSRO      | n/a — `psro-opponent-model.test.ts`                                 | 2026-04-25 |
|                                 | iterations on benchmark scenarios     |                                                                     |            |
| Robustness vs adaptive          | recommended candidate stable under    | [baseline-benchmark-gate](../evaluators/baseline-benchmark-gate.md) | 2026-04-25 |
| counterparty                    | counterparty re-optimization          |                                                                     |            |
| Fairness (Nash / KS / max-min)  | reported per equilibrium candidate    | [fairness-suite](../evaluators/fairness-suite.md)                   | 2026-04-25 |
| Specification-gaming resistance | LCB payoff mode penalizes over-fit to | [fairness-suite](../evaluators/fairness-suite.md)                   | 2026-04-25 |
|                                 | noisy preferences                     |                                                                     |            |
| Runtime (typical)               | seconds for 5 policies / 5 iterations | n/a — deterministic synchronous kernel                              | 2026-04-25 |
| Cost per run                    | $0 LLM-free; with LLM oracle the cost | n/a                                                                 | 2026-04-25 |
|                                 | scales with oracle budget             |                                                                     |            |

## 6. Known limitations

- The proposal-arbitration simulator's fidelity bounds the result; a
  poorly-modeled simulator gives a misleading equilibrium.
- General-sum convergence under replicator dynamics is empirical, not
  guaranteed; use fictitious play for zero-sum subproblems.
- Best-response oracle is heuristic; may miss strict best responses if the
  policy space is poorly conditioned.
- Compute cost grows with policy population; the practical limit is ~10 policies
  per party per run.

## 7. Guardrails

- **Candidate safety gate:** `filterCandidates` on every candidate evaluated
  under any policy.
- **Clause static validation:** inside `filterCandidates`.
- **Redline separation:** redlines apply per-party; PSRO cannot laundered them
  through equilibrium selection.
- **Authority bounds in agent-to-agent runs:** the simulator's acceptance check
  enforces the §179.7.6.3 policy-constrained authority bounds; agent acceptance
  outside its authority is rejected before reaching equilibrium computation.

## 8. References

- `libs/nous/agreement-search/src/psro-opponent-model.ts`
- Lanctot et al. (2017), "A Unified Game-Theoretic Approach to Multiagent
  Reinforcement Learning" (PSRO).
- McMahan, Gordon, Blum (2003), "Planning in the presence of cost functions
  controlled by an adversary".
- `docs/research/bibliography.md` §opponent-modeling