论文标题
有指示链网络上的线性季度随机差异游戏
Linear-Quadratic Stochastic Differential Games on Directed Chain Networks
论文作者
论文摘要
我们在定向链中研究了受到定向链随机微分方程的启发，研究线性二次随机差异游戏，该方程是由Diating，Fouque和Ichiba引入的。我们用有限数量的玩家明确地解决了NASH Equilibria，我们研究了更通用的有限玩家游戏，并混合了定向链相互作用和平均场相互作用。当玩家数量趋于无限时，我们调查并比较了限制中的相应游戏。 该极限的特征是加泰罗尼亚函数，平衡下的动力学是由加泰罗尼亚马尔可夫链描述的无限维高斯过程，有或没有平均场相互作用。
We study linear-quadratic stochastic differential games on directed chains inspired by the directed chain stochastic differential equations introduced by Detering, Fouque, and Ichiba. We solve explicitly for Nash equilibria with a finite number of players and we study more general finite-player games with a mixture of both directed chain interaction and mean field interaction. We investigate and compare the corresponding games in the limit when the number of players tends to infinity. The limit is characterized by Catalan functions and the dynamics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain, with or without the presence of mean field interaction.
