Mean Field Game with Delay: a Toy Model

Linear-Quadratic McKean-Vlasov Stochastic Differential Games

We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and infinite horizon problems with possibly some random coefficients as well as common noise are addressed. We propose a simple direct approach based on weak martingale optimality principle together with a fixed point argument in the space of controls for solving this game problem. The Nash equilibria are characterized in terms of systems of Riccati ordinary different…

用于学习线性二次平均场博弈的探索噪声

Exploration noise for learning linear-quadratic mean field games

研究表明，在线性二次平均场博弈中，适当形式的公共噪声可充当探索噪声，并在无势或单调结构条件下保证虚拟博弈算法收敛。

相关随机游走的赌徒破产问题的鞅方法

Martingale Approach to Gambler's Ruin Problem for Correlated Random Walks

本文利用鞅的可选停时定理研究相关随机游走的赌徒破产问题，推导了特定增量和对称带延迟情况下的破产概率与期望时长的闭式表达式，并开发了针对一般带延迟CRW的鞅技术及对任意模式进行下注的破产概率研究。