• Linear-Quadratic Stochastic Differential Games on Random Directed Networks

    Yichen Feng, Jean-Pierre Fouque, Tomoyuki Ichiba

    Department of Statistics and Applied Probability, South Hall, University of California, Santa Barbara, CA 93106, USA.

    Abstract: The study of linear-quadratic stochastic differential games on directed networks was initiated in Feng, Fouque & Ichiba [7]. 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 [7]. The discussion about stochastic differential games is extended to a random two-sided directed chain and a random directed tree structure.

    Keywords: Linear-quadratic stochastic games, random directed chain network, Nash equilibrium.

    Pages: 79 – 108 | Full PDF Paper