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arXiv · 2011.04279

Linear-Quadratic Stochastic Differential Games on Random Directed Networks

Yichen Feng·Jean-Pierre Fouque·Tomoyuki Ichiba
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Abstract

The study of linear-quadratic stochastic differential games on directed networks was initiated in Feng, Fouque \& Ichiba \cite{fengFouqueIchiba2020linearquadratic}. In that work, the game on a directed chain with finite or infinite players was defined as well as the game on a deterministic directed tree, and their Nash equilibria were computed. The current work continues the analysis by first developing a random directed chain structure by assuming the interaction between every two neighbors is random. We solve explicitly for an open-loop Nash equilibrium for the system and we find that the dynamics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain introduced in \cite{fengFouqueIchiba2020linearquadratic}. The discussion about stochastic differential games is extended to a random two-sided directed chain and a random directed tree structure.

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Yichen Feng, Jean-Pierre Fouque, Tomoyuki Ichiba. 2020-11-05. Linear-Quadratic Stochastic Differential Games on Random Directed Networks. https://arxiv.org/abs/2011.04279

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