Riemannian Manifolds of Asymmetric Equilibria: The Victoria-Nash Geometry

We introduce the Victoria-Nash manifold $\Gamma_{VNAE}(\theta)$ as a smooth submanifold arising from an asymmetric expectation field $F(s;\theta)$. With a Riemannian metric $g(\theta)$ and curvature $K(s;\theta)$ encoding asymmetry via a smooth structural field $\phi(s;\theta)$, $\Gamma_{VNAE}$ generalizes Nash and von Neumann equilibria. We prove existence, smoothness, and invariance using Lefschetz, Tikhonov, and Lyapunov-Morse theory. Classical equilibria are degenerate limits at $K\to 0$.