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Abstract
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 $K\to 0$.
Supplementary materials
Title
Step-by-Step Calculations
Description
A step-by-step demonstration of all the calculations for the proposed formula.
Actions
Title
Graphical Analysis R Code
Description
File containing R code with 4 graphs to graphically prove the theorems in the paper.
Actions
Title
VNAE Gaussian Curvature K R Code
Description
File containing R code with the calculations of the tensor gij and curvature k presented in the paper.
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