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Peer-reviewedCC BY 4.0Mathematics

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

  • Jinjia Chen1
  • Kun Yang2
  • Danhua Liu3
  • Yingchao Wang4
  • Feng Xue2
4 affiliations
  1. 1Binary Business School, Binary University of Management & Entrepreneurship, Puchong 47100, Malaysia
  2. 2Graduate School of Information, Production and Systems, Waseda University, Kitakyushu 808-0135, Japan
  3. 3Graduate School of Business and Finance, Waseda University, Tokyo 169-8050, Japan
  4. 4School of Intelligent Manufacturing and Electrical Engineering, Xinjiang College of Science & Technology, Korla 841000, China
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@article{chen2026equipartition,
  title = {{EquiPartition: Learning Player-Adaptive Deviation Certificates for Complete Enclosure of Approximate Nash Equilibria in Strategic Financial Markets}},
  author = {Jinjia Chen and Kun Yang and Danhua Liu and Yingchao Wang and Feng Xue},
  journal = {Mathematics},
  year = {2026},
  month = nov,
  doi = {10.3390/math14214029},
  url = {https://www.mdpi.com/2227-7390/14/21/4029},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - EquiPartition: Learning Player-Adaptive Deviation Certificates for Complete Enclosure of Approximate Nash Equilibria in Strategic Financial Markets
AU  - Jinjia Chen
AU  - Kun Yang
AU  - Danhua Liu
AU  - Yingchao Wang
AU  - Feng Xue
PY  - 2026
DA  - 2026/11/04
JO  - Mathematics
DO  - 10.3390/math14214029
UR  - https://www.mdpi.com/2227-7390/14/21/4029
AB  - 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.
SN  - 2227-7390
ER  -