arXiv research

Let $M$ and $N$ be Nash manifolds, and $f$ and $g$ Nash maps from $M$ to $N$. If $M$ and $N$ are compact and if $f$ and $g$ are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, $C^infty$ R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash…

The study characterizes Nash maps between semialgebraic sets and their properties.

Hamiltonian cycles found in toroidal maps.

A method is provided to resolve Lie algebroids with singularities.

Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types $\{3^{3},4^{2}\}$, $\{3^{2},4,3,4\}$, $\{6,3,6,3\}$, $\{3^{4},6\}$, $\{4,8^{2}\}$, $\{3,12^{2}\}$, $\{4,6,12\}$, $\{6,4,3,4\}$ exist on the torus. In this article we show the e…

Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.

The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.

Policy mirror ascent achieves Nash equilibrium in mean field games without a population generative model.

New real algebraic maps with prescribed images and compositions are constructed locally like moment maps.

Improves GANs training through game theory.

The Nash-Kuiper Theorem states that the collection of $C^1$-isometric embeddings from a Riemannian manifold $M^n$ into $\mathbb{E}^N$ is $C^0$-dense within the collection of all smooth 1-Lipschitz embeddings provided that $n < N$. This result is now known to be a consequence of Gromov's more general $h$-principle. Ther…

The paper constructs metrics on spheres with families of minimal hypersurfaces.

Nash's theorem proved with Günther's trick

We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…

A generic compact real codimension two submanifold X of C^(n+2) will have a CR structure at all but a finite number of points (failing at the complex jump points J). The main theorem of this paper gives a method of extending the CR structure on the non-jump points X-J to the jump points. We examine a Gauss map from X-J…

Machine learning detects NASH patients from medical claims data.

This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and the existence of a constant rank theorem for such maps. It does so by extending t…

Optimal geometric estimates for Kähler manifolds with bounded Nash entropy

We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser estimates. In particular we discuss questions like continuous dependence of optimal constants and existence and compactness …

The paper examines Nash equilibrium in GANs for stationary Gaussian processes.

New method finds all Nash equilibria via vector optimization.

The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nas…

The paper explores game-theoretic alignment of LLMs with human preferences, finding limitations and conditions.

Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.

In this paper we investigate the existence of ``partially'' isometric immersions. These are maps f:M->R^q which, for a given Riemannian manifold M, are isometries on some sub-bundle H of TM. The concept of free maps, which is essential in the Nash--Gromov theory of isometric immersions, is replaced here by that of H-fr…

This paper tackles global Nash equilibrium in non-convex multi-player games.

A Nash game theory approach allocates capital requirements among financial institutions.

In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substan…

Study on a metric on Hermitian metrics space, proving diffeomorphisms and completeness.

This paper simplifies the Nash Bargaining Solution for use in intellectual property cases.

A new method for RLHF using proximal point Nash learning.

Paper refines royalty determination using Bayesian methods.

Ancient Ricci flows with bounded Nash entropy have uniform Sobolev inequalities.

An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.

We prove that the infinite family of homotopy 4-spheres constructed by Daniel Nash are all diffeomorphic to 4-sphere.

We give geometrical conditions under which there exist extremal functions for the sharp $L^2$-Nash inequality.

In this article, we study local holomorphic isometric embeddings from ${\BB}^n$ into ${\BB}^{N_1}\times... \times{\BB}^{N_m}$ with respect to the normalized Bergman metrics up to conformal factors. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic m…

Study Nash equilibrium between broker and trader in a lit exchange with price impact.

Kuranishi's proof of complex deformation theory revisited

End-to-end model predicts multiagent trajectories using game theory and neural nets.

We obtain global extensions of the celebrated Nash-Kuiper theorem for $C^{1,θ}$ isometric immersions of compact manifolds with optimal Hölder exponent. In particular for the Weyl problem of isometrically embedding a convex compact surface in 3-space, we show that the Nash-Kuiper non-rigidity prevails upto exponent $θ<1…

The paper proposes a method to learn continuous-action graphical games from perturbed equilibria.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

Improved SEG method converges to Nash equilibrium in bilinear games.

This research uses reinforcement learning to find optimal emission offsets in greenhouse gas markets.

Study shows how multiple traders can trade together without excessive price impact.

We prove that each sub-Riemannian manifold can be embedded in some Euclidean space preserving the length of all the curves in the manifold. The result is an extension of Nash $C^1$ Embedding Theorem. For more general metric spaces the same result is false, e.g., for Finsler non-Riemannian manifolds. However, we also sh…

Study Nash equilibrium in mean field portfolio games with random market parameters.