Linear-Quadratic Stochastic Differential Games on Random Directed Networks
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.
Cite
@article{arxiv.2011.04279,
title = {Linear-Quadratic Stochastic Differential Games on Random Directed Networks},
author = {Yichen Feng and Jean-Pierre Fouque and Tomoyuki Ichiba},
journal= {arXiv preprint arXiv:2011.04279},
year = {2020}
}
Comments
24 pages. arXiv admin note: text overlap with arXiv:2003.08840