arXiv research

Optimal geometric estimates for Kähler manifolds with bounded Nash entropy

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

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

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

New formulas derived for scalar curvature in generalized Ricci flow.

The paper establishes bounds for Ricci flows using entropy and heat kernel methods.

Study of entropy-regularized LQG MFGs with exploratory actions.

Compact RCD spaces derived from singular Kahler metrics on 3D projective varieties.

Paper proves volume growth estimate for steady gradient Ricci solitons.

The article examines entropy-information inequalities for continuous-time Markov chains under curvature-dimension conditions.

Let $(M^n, g)$ be a complete Riemannian manifold with $Rc\geq -Kg$, $H(x, y, t)$ is the heat kernel on $M^n$, and $H= (4πt)^{-\frac{n}{2}}e^{-f}$. Nash entropy is defined as $N(H, t)= \int_{M^n} (fH) dμ(x)- \frac{n}{2}$. We studied the asymptotic behavior of $N(H, t)$ and $\frac{\partial}{\partial t}\Big[N(H, t)\Big]$ …

Local Sobolev inequality on Ricci flows with applications.

Uniform bounds prove connection between Kähler metrics and RCD spaces.

Ancient Ricci flows with asymptotic solitons have uniform bounds and inequalities.

In this paper, we prove the concavity of $p$-entropy power of probability densities solving the $p$-heat equation on closed Riemannian manifold with nonnegative Ricci curvature. As applications, we give new proofs of $L^p$-Euclidean Nash inequality and $L^p$-Euclidean Logarithmic Sobolev inequality, moreover, an improv…

Study geometric bounds on generalized Ricci flow.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

In 1870s, L. Boltzmann proved the famous $H$-theorem for the Boltzmann equation in the kinetic theory of gas and gave the statistical interpretation of the thermodynamic entropy. In 2002, G. Perelman introduced the notion of $W$-entropy and proved the $W$-entropy formula for the Ricci flow. This plays a crucial role in…

Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.

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…

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…

Machine learning detects NASH patients from medical claims data.

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…

Study smooth convergence of metric flows from $\mathbb{F}$-limits.

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

A method is provided to resolve Lie algebroids with singularities.

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…

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

Paper refines royalty determination using Bayesian methods.

A new method for RLHF using proximal point Nash learning.

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.

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

Kuranishi's proof of complex deformation theory revisited

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

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…

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.

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

A new algorithm reduces memory and computational needs for reinforcement learning.

GANs may not have Nash equilibria, but proximal training can find solutions.

We introduce a new loss function for evaluating forecasts and estimate models using it.