A quadratic Mean Field Games model for the Langevin equation

带共同噪声的Hilbert空间中的线性二次平均场博弈与主方程

Linear quadratic Mean Field Games and Master Equations in Hilbert spaces with common noise

本文研究无限维Hilbert空间中带共同噪声的线性二次平均场博弈，通过算子值Riccati方程刻画温和解，建立全局存在唯一性，并证明主方程解恢复值函数及验证定理。

关于多玩家线性二次闭环博弈的若干注记

Some remarks on Linear-quadratic closed-loop games with many players

本文研究多玩家线性二次闭环博弈的 Nash 系统，在稀疏图和广义平均场两种设定下证明解的存在性、收敛性及 ε-Nash 均衡性质，并为 N 趋于无穷的收敛分析奠定基础。

具有非二次哈密顿量的平均场博弈回溯问题的Hölder稳定性估计

Hölder Stability Estimate for a Retrospective Problem of Mean Field Games With a Non-Quadratic Hamiltonian

本文利用Carleman估计方法，将平均场博弈回溯问题的Hölder稳定性估计与唯一性结果从二次哈密顿量情形推广到非二次哈密顿量情形。

带拥塞的二次Hamilton平稳平均场对策的存在性

Existence for stationary mean field games with quadratic Hamiltonians with congestion

本文研究了J. -提出的平稳平均场对策模型解的存在唯一性M. Lasry和P. - L.狮子该模型的特点是二次哈密尔顿可能奇异的拥塞效应。由于一类新的先验界，结合延拓方法，我们证明了光滑解的存在性在任意维。

Linear-Quadratic Mean Field Games of Controls with Non-Monotone Data

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the interaction is via the joint law of both the state and control. By the stochastic maximum principle, we first analyze the limiting behavior of the representative player and obtain his/her optimal control in a feedback form with the given distributional flow of the population and its control. The mean field equilibrium is determined by the Nash certainty equival…

Hilbert 空间中的线性二次平均场博弈

Linear-Quadratic Mean Field Games in Hilbert spaces

本文首次在无限维 Hilbert 空间中发展线性二次平均场博弈理论，通过均值依赖将系统简化为 Riccati 方程与抽象发展方程的耦合系统，利用逼近程序证明解的存在唯一性，并应用于带延迟的生产规划问题。

Properties of moments of density for nonlocal mean field game equations with a quadratic cost function

We consider mean field game equations with an underlying jump-diffusion process $X_t$ for the case of a quadratic cost function and show that the expectation and variance of $X_t$ obey second-order ordinary differential equations with coefficients depending on the parameters of the cost function. Moreover, for the case of pure diffusion, the characteristic function and the fundamental solution of the equation for the probability density can only be expressed in terms of the expectation ${\mathbb E}$ and the variance ${\mathbb V}$ of the process $X_t$, so that the moments of any order depend on…

二次哈密顿量的平均场博弈方程：一种特定方法

Mean field games equations with quadratic Hamiltonian: a specific approach

通过变量变换将二次哈密顿量下的平均场博弈方程简化为更简单的耦合偏微分方程组，并基于此构造单调格式求解，提出有效数值方法并完成数值实验。