Linear-Quadratic Stochastic Differential Games on Directed Chain Networks
Linear-Quadratic Stochastic Differential Games on Directed Chain Networks
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发表时间：
2020-03
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通讯作者：
Yichen Feng;J. Fouque;Tomoyuki Ichiba
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作者：
Yichen Feng;J. Fouque;Tomoyuki Ichiba
我们受 Detering、Fouque 和 Ichiba 引入的有向链随机微分方程的启发，研究有向链上的线性二次随机微分博弈。我们明确地求解了有限数量玩家的纳什均衡，并研究了更一般的有限玩家博弈，其中混合了有向链相互作用和平均场相互作用。我们在玩家数量趋于无穷大的情况下，对相应的游戏进行了调查和比较。极限由 Catalan 函数表征，平衡下的动力学是由 Catalan 马尔可夫链描述的无限维高斯过程，存在或不存在平均场相互作用。
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.