We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs＇ equation. Links between supersolutions and epicontingent solutions to Isaacs＇ equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the HCO problem from contingent formulation of Isaacs＇ equation.