The paper resolves singular foliations through a series of blowups.
problem Singular foliations that cannot be resolved directly.
method Applying Nash modifications to the universal Lie ∞-algebroid of a singular foliation.
result Any singular foliation becomes a Debord foliation after one blowup.
Policy mirror ascent achieves Nash equilibrium in mean field games without a population generative model.
problem Achieving Nash equilibrium in mean field games without a population generative model.
method Policy mirror ascent, contractive operator, single-path TD learning.
result Policy mirror ascent converges to Nash equilibrium within O ~ ( ε − 2 ) \widetilde{\mathcal{O}}(\varepsilon^{-2}) O ( ε − 2 ) samples. New assumptions and algorithm solve offline two-player zero-sum Markov games.
problem Solving offline two-player zero-sum Markov games under insufficient assumptions.
method Proposed unilateral concentration assumption and pessimism-type algorithm.
result Algorithm efficiently learns Nash equilibrium under unilateral concentration.
Let M M M and N N N be Nash manifolds, and f f f and g g g Nash maps from M M M to N N N . If M M M and N N N are compact and if f f f and g g g are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, C i n f t y C^infty C i n f t y 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
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
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.
problem Detecting undiagnosed NASH patients for screening and management.
method Gradient-boosted decision trees trained on administrative medical claims data.
result Model precision for NASH detection is significantly higher than NASH incidence.
Optimal geometric estimates for Kähler manifolds with bounded Nash entropy
problem Optimal geometric estimates for compact Kähler manifolds
method Proving Sobolev-type inequality and local volume noncollapsing with optimal exponents
result Uniformly bounded q q q -Nash entropy The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
problem Existence and uniqueness of Nash equilibrium in GANs for stationary Gaussian processes.
method Analyzes the existence of Nash equilibrium in GANs for stationary Gaussian processes, considering different discriminator families.
result The existence of Nash equilibrium depends on the discriminator family and symmetry properties of the generator family.
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
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…
Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.
problem Learning Nash equilibria in zero-sum stochastic games is computationally expensive.
method Entropy-regularized soft policies for Q-function updates.
result Algorithm converges to Nash equilibrium under certain conditions.
The study characterizes Nash maps between semialgebraic sets and their properties.
problem Existence of surjective Nash maps between semialgebraic sets.
method Characterization of semialgebraic subsets and their images under Nash maps.
result Characterization of semialgebraic sets that are Nash images of the unit ball.
A method is provided to resolve Lie algebroids with singularities.
problem Resolving Lie algebroids with singular points.
method Nash-type blow-up construction for Lie algebroids.
result A short exact sequence is established linking the blow-up to Lie algebroids.
A Nash game theory approach allocates capital requirements among financial institutions.
problem Allocating systemic risk measures among financial institutions.
method Proposes a Nash allocation rule inspired by game theory.
result Provides sufficient conditions for the existence and uniqueness of Nash allocation rules.
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.
problem Limited application of Nash Bargaining Solution in assigning intellectual property damages.
method Normalizes the Nash Bargaining Solution and provides a methodology for determining bargaining weight.
result Clarifies the application of Nash Bargaining Solution to specific case facts.
Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.
problem Finding a fair Nash equilibrium in group decision-making.
method Introduces entropy-norm space for geometric selection of strict Nash equilibria.
result The closest entropy-norm pair to the largest entropy-norm pair in rescaled space is the most suitable equilibrium.
Paper refines royalty determination using Bayesian methods.
problem Determining a reasonable royalty with risk and uncertainty.
method Bayesian Cost approach to refine Nash Bargaining Solution.
result Nash Bargaining Solution emerges as more reliable.
A new method for RLHF using proximal point Nash learning.
problem Capturing real human preferences in RLHF.
method Proximal point Nash learning, embedding self-play updates into a proximal point framework.
result High-probability last-iterate convergence for the combined method.
An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.
Ancient Ricci flows with bounded Nash entropy have uniform Sobolev inequalities.
problem Bounding Nash entropy in ancient Ricci flows.
method Uniformly bounded Nash entropy implies uniform bounds on the ν-functional, leading to uniform logarithmic and Sobolev inequalities.
result Uniform logarithmic and Sobolev inequalities on ancient Ricci flows with bounded Nash entropy.
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 L^2 L 2 -Nash inequality.
The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.
problem Existence and uniqueness of Nash equilibria in multiplicative performance criteria games.
method General characterization of Nash equilibria for a large class of utility functions.
result Existence and uniqueness of Nash equilibria for arbitrary initial wealth vectors.
Kuranishi's proof of complex deformation theory revisited
problem Existence of complex deformations on compact complex manifolds
method Hamilton-Nash-Moser implicit function theorem
result Revisits classical proof with modern tools
Study Nash equilibrium between broker and trader in a lit exchange with price impact.
problem Optimizing trading strategies between informed and uninformed traders with broker's inventory penalties.
method Characterized Nash equilibrium through FBSDEs, solved explicitly.
result Explicit solution to trading strategies of broker and informed trader.
We obtain global extensions of the celebrated Nash-Kuiper theorem for C 1 , θ C^{1,θ} 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…
PAPAL algorithm finds mixed Nash equilibria in continuous games.
problem Finding mixed Nash equilibria in non-convex, non-concave games.
method Particle-based Primal-Dual Algorithm (PAPAL) for weakly entropy-regularized min-max optimization.
result PAPAL offers non-asymptotic convergence guarantees for ε ε ε -mixed Nash equilibrium. Improved SEG method converges to Nash equilibrium in bilinear games.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
This research uses reinforcement learning to find optimal emission offsets in greenhouse gas markets.
problem Finding optimal emission offsets in greenhouse gas markets to control excess emissions.
method Utilized reinforcement learning, specifically Nash-DQN, to estimate market Nash equilibria.
result Emitting firms can achieve significant financial savings by abiding by the Nash equilibria found in the market.
Study shows how multiple traders can trade together without excessive price impact.
problem Coordination issues in trading to exploit a common signal.
method Closed-loop Nash competition model for stochastic differential games.
result Excessive trading reduced but not significantly for practical parameters.
Study Nash equilibrium in mean field portfolio games with random market parameters.
problem Modeling wealth and relative performance in competitive financial markets.
method Martingale optimality principle approach to characterize Nash equilibrium in mean field FBSDE.
result Unique Nash equilibrium found under weak interaction assumption and market parameters independence.
A new algorithm reduces memory and computational needs for reinforcement learning.
problem Memory and computational inefficiency in model-free reinforcement learning.
method Memory-Efficient Nash Q-Learning (ME-Nash-QL) for two-player zero-sum games.
result Proves ME-Nash-QL reduces space and sample complexity for tabular and long-horizon cases.
GANs may not have Nash equilibria, but proximal training can find solutions.
problem Existence of Nash equilibria in GANs optimization.
method Proximal training approach to find solutions.
result Proximal training finds solutions to GAN problems.
We introduce a new loss function for evaluating forecasts and estimate models using it.
problem Lack of a decision-theoretic foundation for evaluating forecasts using the Nash-Sutcliffe efficiency.
method We introduce and analyze the Nash-Sutcliffe loss function and its application in estimating models.
result Nash-Sutcliffe loss provides a decision-theoretic foundation for evaluating and estimating models.
We prove that for any complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, if the Nash inequality is satisfied, then it is diffeomorphic to R n R^{n} R n l.
The paper proves inequalities on Finsler manifolds under Ricci curvature bounds.
problem Proving ( p , q ) (p, q) ( p , q ) -Sobolev and Nash inequalities on Finsler metric measure manifolds. method Global p p p -Poincaré inequality, ( p , q ) (p, q) ( p , q ) -Sobolev inequality, Nash inequality derivation. result Established global optimal ( p , q ) (p, q) ( p , q ) -Sobolev inequality with a sharp constant. This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric embeddings.
Study Nash competition among dealers quoting prices to clients with unknown trading motives.
problem Adverse selection and inventory costs in dealer-client interactions.
method Analyzes one-shot Nash competition with unknown client type and inventory constraints.
result Unique symmetric Nash equilibrium exists and can be characterized by a nonlinear ODE.
Study Nash equilibrium in non-zero-sum game with Bermudan strategies.
problem Optimizing pay-offs in non-linear non-zero-sum games.
method Recursive construction to find Nash equilibrium.
result Existence of Nash equilibrium in non-zero-sum game.
Given a multifunction from X X X to the k − k- k − fold symmetric product S y m k ( X ) Sym_k(X) S y m k ( X ) , we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…
In this note, we present an existence result of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity…
The paper analyzes game theory in convertible contracts during liquidity events.
problem Optimizing payments in convertible contracts during liquidity events.
method Defined a general model for games, showed non-existence of pure strategy Nash equilibria, developed algorithms for computing equilibria.
result Optimum pure strategy Nash equilibria exist when all contracts are of the same type (SAFE).
Nash integrates covariate-specific side info into sparse regression via neural networks.
problem Sparse linear regression struggles with covariates exhibiting structure or coming from heterogeneous sources.
method Neural Adaptive Shrinkage (Nash) framework that integrates side information into sparse regression via neural networks. Uses split variational empirical Bayes algorithm.
result Nash improves accuracy and adaptability over existing methods in real data experiments.
In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We p…
A RL approach finds Nash equilibrium for turn-based zero-sum games.
problem Finding Nash equilibrium in two-player turn-based zero-sum games.
method EIS method combining exploration, policy improvement, and supervised learning.
result EIS method finds an ε-approximate value function of Nash equilibrium in O(ε^(-(d+4))) steps.
The paper solves portfolio optimization problems with risk constraints.
problem Maximizing utility while ensuring a certain wealth threshold with risk constraints.
method Derives Nash equilibria for two agents and characterizes them for more than two agents.
result Characterizes Nash equilibria for different cases of competition probabilities.