相关论文: Variational Inequality Approach to Stochastic Nash…

These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…

The equilibrium selection problem in the variational Generalized Nash Equilibrium Problem (v-GNEP) has been reported as an optimization problem defined over the solution set of v-GNEP, called in this paper the lower-level v-GNEP. However,…

This paper investigates full stability properties for \emph{variational Nash equilibriums} of a system of parametric nonconvex optimal control problems governed by semilinear elliptic partial differential equations. We first obtain some new…

This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus…

The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…

We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge…

This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal…

We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic differential equations, both in Ito and in Stratonovich form.…

We study one-shot Nash competition between an arbitrary number of identical dealers that compete for the order flow of a client. The client trades either because of proprietary information, exposure to idiosyncratic risk, or a mix of both…

In this article we study some problems related to the incompressible 3D Navier-Stokes equations from the point of view of Lebesgue spaces of variable exponent. These functional spaces present some particularities that make them quite…

This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach…

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…

One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement…

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal…

Variational inequalities are a broad formalism that encompasses a vast number of applications. Motivated by applications in machine learning and beyond, stochastic methods are of great importance. In this paper we consider the problem of…

Martingale solutions of stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains, driven by the L\'evy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered.…

We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable…