Generated Direction Mapping (GDM) for Equilibrium and Game Theory: A Formal Framework

We introduce Generated-Direction Mapping (GDM) for equilibrium and game the-ory. Let X ⊂ Rn be feasible set, X = ∪iXi stratified, and TX (u) = ∪iTXi (u) with gaps.Classical theory assumes any direction in TX (u) is generable, but micro is stratifiedand incomplete. We define micro decision mapping D : X ×X → Rn and macro gener-ation D(x, u) → TD(u) under Admissibility Condition. We prove: (i) Only admissibleD(x, u) generates TD(u)̸ = ∅, (ii) If not admissible, TD(u) = ∅, (iii) If admissible,TD(u) = ATX (u). Thus only admissible micro generates macro.This foundation leads to Generated Direction Equilibrium (GDE) and GeneratedDirection Game Theory Model (GDGT), where equilibrium is defined only by gen-erated admissible deviations. As an application, this framework provides the formalmechanism for microfoundations of macroeconomic stabilization.