Building upon the dynamic programming principle for set-valued functions arising from many applications, we will present a new notion of set-valued PDEs. The key component is a set-valued Ito formula, characterizing the flows on the surface of the dynamic sets. In the context of multivariate control problems, we establish the wellposedness of the set-valued HJB equations, which extends the standard HJB equations in the scalar case to the multivariate case. As an application, we discuss moving scalarization, constructed using the classical solution of the set-valued HJB equation. Additionally, we introduce the concept of set values for games under Nash equilibrium, along with the corresponding PDE, and explore its geometric properties. The talk is based on joint work with Jianfeng Zhang and ongoing work joint with Nizar Touzi and Jianfeng Zhang.