Linear Quadratic Nash Differential Games of Stochastic Singular Systems

Zhou Haiying (), Zhu Huainian and Zhang Chengke
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Zhou Haiying: School of Management, Guangdong University of Technology, Guangzhou510520, China
Zhu Huainian: School of Management, Guangdong University of Technology, Guangzhou510520, China
Zhang Chengke: School of Economics and Commerce, Guangdong University of Technology, Guangzhou510520, China

Journal of Systems Science and Information, 2014, vol. 2, issue 6, 553-560

Abstract: In 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.

Keywords: stochastic singular systems; Nash differential games; finite-time; horizon; infinite-time horizon (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:2:y:2014:i:6:p:553-560:n:6

DOI: 10.1515/JSSI-2014-0553

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