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Creators/Authors contains: "Yichen Feng, Jean-Pierre Fouque"

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  1. (, Journal of mathematics and statistical science)
    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. 
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    Accepted Manuscript Full Text Available
  2. (, Journal of mathematics and statistical science)
    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 in- teraction 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 dy- namics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain, with or without the presence of mean field interaction. 
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    Accepted Manuscript Full Text Available