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| Autore principale: | |
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| Natura: | Recurso digital |
| Lingua: | inglese |
| Pubblicazione: |
Zenodo
2026
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| Soggetti: | |
| Accesso online: | https://doi.org/10.5281/zenodo.19543427 |
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Sommario:
- <p>We develop the complete Riemannian geometry of Victoria–Nash asymmetric equilibrium manifolds (VNAE) for $n$-player games. The metric \(g_{ij} = \iota_i \iota_j \delta_{ij} + \varepsilon H_{ij}(V,\iota)\) yields explicit Levi-Civita connection \(\Gamma^k_{ij}\), Riemann tensor \(R^i_{\,jkl}\) with fourth-order $V$-derivative cancellation, Ricci tensor <br>\(R_{ij} \approx \kappa\bigl(\iota_{i,j} \iota_i - \kappa \partial_i^2 \iota_i\bigr) \delta_{ij}\), and scalar curvature <br>\(K_s \approx \sum_{i<j} \iota_i \iota_j \det H_{ij}^s + O(\varepsilon^2)\). Positive/negative/zero signatures classify stability geometrically. The Lyapunov–Morse functional \(\mathcal{L}\) satisfies \(\frac{d^2}{dt^2}\mathcal{L}\big|_{\mathrm{VNAE}} \approx -2 \operatorname{Ric}(\dot{s}^\perp,\dot{s}^\perp)\) along gradient flows, establishing Ricci curvature as the normal contraction rate. Classical Nash, von Neumann’s minimax theorem, and Lyapunov stability emerge as degenerate flat limits as \(\varepsilon\to0\). </p>