Regulating All Induced Equilibria: Counterexample-Coupled Incentive–Certificate Synthesis for Financial Stability

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.