arXiv research

New method finds all Nash equilibria via vector optimization.

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

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

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

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

Actor-critic finds Nash in mean-field games with linear-quadratic costs.

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

Study Nash equilibrium in non-zero-sum game with Bermudan strategies.

Gradient-based Nikaido-Isoda function helps find Nash equilibria efficiently.

Algorithm finds Nash equilibria in complex games with function approximation.

Kuranishi's proof of complex deformation theory revisited

Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.

Harmonic functions stable under small changes.

Distributed strategic learning has been getting attention in recent years. As systems become distributed finding Nash equilibria in a distributed fashion is becoming more important for various applications. In this paper, we develop a distributed strategic learning framework for seeking Nash equilibria under stochastic…

A RL approach finds Nash equilibrium for turn-based zero-sum games.

Given a multifunction from $X$ to the $k-$fold symmetric product $Sym_k(X)$, 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…

Study optimal transport for robust optimization, showing how adversary's strategy relates to regularization.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

We consider a market impact game for $n$ risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a mean-variance functional of their costs or to maximize the expected exponential u…

Paper examines stability of non-proper smooth functions.

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 paper proves the concavity of $p$-entropy power and applies it to functional inequalities.

Proposes a new algorithm to find local Nash equilibria in zero-sum games.

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

Nash's theorem proved with Günther's trick

This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in expert strategies, we introduce a new objective function that directly pits expert…

Machine learning detects NASH patients from medical claims data.

Optimal geometric estimates for Kähler manifolds with bounded Nash entropy

Transient market impact explained via Nash equilibrium in a game.

Optimal algorithm for two-player zero-sum games with linear parameterization.

In this paper, we prove the equivalent of ultracontractive bound of heat semigroup or the uniform upper bound of the heat kernel with the Nash inequality, Log-Sobolev inequalities on graphs. We also show that under the assumption of volume growth and nonnegative curvature $CDE'(n,0)$ the Sobolev inequality, Nash inequa…

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

New RL algorithms find SNE in Markov games with myopic followers.

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…

Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.

In this paper both we establish the best constants for the Nash inequalities on the standard unit sphere $\mathbb{S}^n$ of $\mathbb{R}^{n+1}$ and we give answers on the existence of extremal functions on the corresponding problems. Also we study the problem of the best constants in the case, where the data are invarian…

Global Nash-Kuiper theorem extended for compact manifolds with optimal Hölder exponent.

Extends SORTE to multivariate risk functions.

Policy optimization converges to Nash equilibria in zero-sum LQ games.

In this paper, we analyze Nash equilibria 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 production. We set out a…

We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entangl…

Study Euler obstruction of 1-forms on determinantal singularities.

This article presents a proof of the existence of Bertrand-Nash equilibrium prices with multi-product firms and under the Logit model of demand that does not rely on restrictive assumptions on product characteristics, firm homogeneity or symmetry, product costs, or linearity of the utility function. The proof is based …

Community detection in graphs has been the subject of many algorithms. Recent methods want to optimize a modularity function which shows a maximum of relationships within communities and found a minimum of inter-community relations. these algorithms are applied to unipartite, multipartite and directed graphs. However, …

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

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

New algorithm finds Nash equilibrium in multi-agent games.