Linear Quadratic Nash Differential Games of Stochastic Singular Systems with Markovian Jumps

2019 ◽  
Vol 45 (3) ◽  
pp. 651-660
Author(s):  
Bin Liu ◽  
Xin Wang
Keyword(s):  
Differential Games ◽  
Singular Systems ◽  
Linear Quadratic ◽  
Stochastic Singular Systems ◽  
Nash Differential Games

scholarly journals Linear Quadratic Nash Differential Games of Stochastic Singular Systems

2014 ◽  
Vol 2 (6) ◽  
pp. 553-560
Author(s):  
Haiying Zhou ◽  
Huainian Zhu ◽  
Chengke Zhang
Keyword(s):  
Differential Games ◽  
Finite Time ◽  
Time Horizon ◽  
Singular Systems ◽  
Existence Condition ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Finite Time Horizon ◽  
Stochastic Singular Systems ◽  
Nash Differential Games

AbstractIn this paper, we deal with the Nash differential games of stochastic singular systems governed by Itô-type equation in finite-time horizon and infinite-time horizon, respectively. Firstly, the Nash differential game problem of stochastic singular systems in finite time horizon is formulated. By applying the results of stochastic optimal control problem, the existence condition of the Nash strategy is presented by means of a set of cross-coupled Riccati differential equations. Similarly, under the assumption of the admissibility of the stochastic singular systems, the existence condition of the Nash strategy in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. The results show that the strategies of each players interact.

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