Regulating All Induced Equilibria: Counterexample-Coupled Incentive–Certificate Synthesis for Financial Stability
4 affiliations
- 1Binary Business School, Binary University of Management & Entrepreneurship, Puchong 47100, Malaysia
- 2Graduate School of Information, Production and Systems, Waseda University, Kitakyushu 808-0135, Japan
- 3School of Intelligent Manufacturing and Electrical Engineering, Xinjiang College of Science & Technology, Korla 841000, China
- 4Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
Abstract
Regulatory instruments alter institutional payoffs, but they do not choose which equilibrium a decentralized financial system will realize. A policy that appears safe at one computed response can therefore coexist with an unobserved fire-sale or funding-run outcome. We pose policy construction as a set-containment requirement: every approximate Nash equilibrium of the regulated game must remain inside a buffered stability target. EquiImplement enforces this requirement with state-dependent mixtures of admissible unilateral deviations over the target complement. When policy features enter payoffs affinely, holding this proof object fixed gives affine inequalities in the regulatory vector and a concave minimum margin, producing a convex semi-infinite policy subproblem. A rigorous regional separator locates the weakest-covered state, and the same verified counterexample drives both the next policy solve and certificate revision. A preset outer-iteration budget gives finite execution and one of three outputs: globally certified containment, budget infeasibility within the prescribed incentive–certificate family, or an unresolved status. The evaluation covers 330 fire-sale and rollover/run games. At the default budget, EquiImplement attains full-stability rates of 95.0%, 85.6%, and 92.5%, while reducing the worst-equilibrium violation from 0.037 for the strongest non-oracle baseline to 0.016. The mean regulatory cost over returned budget-feasible evaluation policies decreases from 0.119 to 0.113. Further analyses relate certification difficulty to stability-target tightness, leverage, market depth, liquidity buffers, and coordination strength. The results show that a deviation-based proof object can serve directly as an optimization interface for financial regulation under equilibrium multiplicity.
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BibTeX
@article{chen2026regulating,
title = {{Regulating All Induced Equilibria: Counterexample-Coupled Incentive–Certificate Synthesis for Financial Stability}},
author = {Jinjia Chen and Yulun Chen and Kun Yang and Xingyu Zhou and Yingchao Wang and Feng Xue and Tianfu Li},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203835},
url = {https://www.mdpi.com/2227-7390/14/20/3835},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Regulating All Induced Equilibria: Counterexample-Coupled Incentive–Certificate Synthesis for Financial Stability
AU - Jinjia Chen
AU - Yulun Chen
AU - Kun Yang
AU - Xingyu Zhou
AU - Yingchao Wang
AU - Feng Xue
AU - Tianfu Li
PY - 2026
DA - 2026/10/21
JO - Mathematics
DO - 10.3390/math14203835
UR - https://www.mdpi.com/2227-7390/14/20/3835
AB - Regulatory instruments alter institutional payoffs, but they do not choose which equilibrium a decentralized financial system will realize. A policy that appears safe at one computed response can therefore coexist with an unobserved fire-sale or funding-run outcome. We pose policy construction as a set-containment requirement: every approximate Nash equilibrium of the regulated game must remain inside a buffered stability target. EquiImplement enforces this requirement with state-dependent mixtures of admissible unilateral deviations over the target complement. When policy features enter payoffs affinely, holding this proof object fixed gives affine inequalities in the regulatory vector and a concave minimum margin, producing a convex semi-infinite policy subproblem. A rigorous regional separator locates the weakest-covered state, and the same verified counterexample drives both the next policy solve and certificate revision. A preset outer-iteration budget gives finite execution and one of three outputs: globally certified containment, budget infeasibility within the prescribed incentive–certificate family, or an unresolved status. The evaluation covers 330 fire-sale and rollover/run games. At the default budget, EquiImplement attains full-stability rates of 95.0%, 85.6%, and 92.5%, while reducing the worst-equilibrium violation from 0.037 for the strongest non-oracle baseline to 0.016. The mean regulatory cost over returned budget-feasible evaluation policies decreases from 0.119 to 0.113. Further analyses relate certification difficulty to stability-target tightness, leverage, market depth, liquidity buffers, and coordination strength. The results show that a deviation-based proof object can serve directly as an optimization interface for financial regulation under equilibrium multiplicity.
SN - 2227-7390
ER -