regaining viability dominance

This paper develops a control-theoretic framework for understanding how dominant actors preserve or regain influence under changing regulatory constraints. Using viability theory and differential game formulations, we model regulation as a dynamic reshaping of admissible state–control sets rather than direct intervention in system dynamics. We show that dominance is a geometric property of the induced viability kernel and is generally lost under constraint tightening unless the actor adapts by internalizing the new constraints, anticipating kernel contraction, or migrating to alternative admissible regimes. A regulator–actor Stackelberg game is formulated in which the regulator controls feasibility via constraint design, while the actor optimizes within the resulting kernel. The analysis establishes conditions under which dominance can be preserved or re-established without violating constraints, and explains the observed irreversibility (hysteresis) of dominance loss in regulated systems. The results unify viability theory, constrained control, and regulatory dynamics, with implications for economics, finance, and complex socio-technical systems.