EquiPartition: Learning Player-Adaptive Deviation Certificates for Complete Enclosure of Approximate Nash Equilibria in Strategic Financial Markets

Strategic financial markets can admit multiple approximate Nash equilibria with materially different liquidation and price-impact regimes. Returning one equilibrium cannot exclude a more stressed alternative, yet complete enclosure becomes expensive when the profitable deviator changes inside a search region. We propose EquiPartition, a learning-augmented branch-and-bound method based on player-adaptive deviation certificates. The certificate combines institution-specific unilateral-deviation atoms through state-dependent Bernstein weights, while an outward-rounded verifier alone authorizes exclusion. Inconclusive proposals undergo bounded repair or conservative subdivision, so prediction quality affects efficiency but not the complete ε-Nash outer-enclosure guarantee. On the controlled and multi-institution synthetic one-period fire-sale markets, the finite recorded-reference audit retained all recorded high-precision reference-equilibrium components and found no accepted exclusion intersecting them. Relative to Nash-B&B, Predict+Repair reduced proof-tree nodes by 83.3% and 83.9%, unresolved volume by 75.8% and 69.0%, and mean capped runtime by 40.5% and 20.2%; it completed 113 of 120 multi-institution instances versus 103 for Nash-B&B. The same finite recorded-reference audit retained all recorded crisis components under the financial stress shifts. Runtime decomposition showed that amortized proposals avoided repeated neutral-start optimization and offset repair and verification costs. EquiPartition reduces proof fragmentation while preserving verifier-based completeness.