docs(audit): game-theory operator plan + numerically verified math audit

[gstoner]

Summary

Plan-stage tranche for a game-theory operator family in Tessera, sourced from the Faigle Mathematical Game Theory lecture-note review plus the maintainer's refined-equilibria list (SPE, Bayesian, k-resilient, correlated, bounded rationality, Preference-CFR).

docs/audit/compiler/GAME_THEORY_PLAN.md (follows the RIEMANNIAN_OT_PLAN.md convention):

• Subset zeta/Möbius as an FFT-sibling radix-2 butterfly riding the existing spectral_candidates arbiter lane; one weight-parameterized semivalue op covering Shapley/Banzhaf/interaction indices; boltzmann_value as n-head online-softmax over the coalition lattice; equilibria on the existing custom_root/sparsemax implicit-diff seam.
• G0–G6 phasing, with two sanctioned guardrail overrides (maintainer, 2026-08-15) argued in §4.6: a test-only differential-oracle dependency group, and a generic tessera.butterfly_transform (G1b) consolidating tiling already duplicated by the spectral FFT lane (Decision Apple GPU: Gumbel-max inference sampler (#18-safe, reproducible) #31). The overrides for a runtime LP dependency and a tessera_game dialect are explicitly declined.
• §9 developer-capability surface across four user populations (explainability/SHAP, MARL/PSRO, mechanism design, governance), with three genuinely new items: the sampled-estimator CI contract, exploitability as a first-class metric op, and the Python-layer Game protocol.

research/game_theory/ — the 27-check numerical verification harness (all passing; numpy-only). Two plan claims were corrected by measurement:

• The §6 fp32 wall is sign-structure-dependent: nonnegative monotone characteristic functions (real cooperative games) are the worst case — roundtrip error 0.15 at n=20, pure noise at n=24 — and fp32 storage of the zeta, not just accumulation, is the failure. Zeta→consumer fusion is therefore a correctness feature (Decision docs: scope GPU-resident activations / persistent device-handle model #32).
• Hazard H2 demonstrated live: two consecutive plausible-but-wrong Blum–Mansour swap-regret implementations (violations 0.226, 0.200), neither caught by any algebraic invariant; corrected version reaches CE-violation 0.0000. This upgrades the differential-oracle requirement from argued to evidenced.

Test plan

• python3 research/game_theory/verify_game_theory_plan.py — 27/27 checks pass
• pre-push generated-doc drift gate passes (docs-only change; no generated dashboards touched)
• Maintainer review of §11 open questions (build-order call: G1-first vs G2-first)

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