We present the salient features of a min-max game theory developed in the context of coupled PDE's with an
interface. Canonical applications include linear fluid-structure interaction problem modeled by Oseen's equations coupled
with elastic waves. We shall consider two models for the structures: elastic and visco-elastic. Control and disturbance are
allowed to act at the interface between the two media. The sought-after saddle solutions are expressed in a pointwise
feedback form, which involves a Riccati operator; that is, an operator satisfying a suitable non-standard Riccati
differential equation. Motivations, applications as well as a brief historical account are also provided.