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Linear-Quadratic Stochastic Differential Games on Random Directed Networks

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 نشر من قبل Jean-Pierre Fouque
 تاريخ النشر 2020
  مجال البحث
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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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