Brief paper: nash strategy for multiparameter singularly perturbed Markov jump stochastic systems

This study investigates Nash games for a class of multiparameter singularly perturbed stochastic systems governed by Itôôs differential equation with Markov jump parameters. First, in order to obtain Nash equilibrium strategies, cross-coupled stochastic algebraic Riccati equations (CSAREs) are formulated. Moreover, necessary condition for the existence of solution for CSAREs is also developed. It is noteworthy that this is the first time that conditions for the existence of stochastic equilibria have been derived based on the solutions of sets of CSAREs. After establishing an asymptotic structure with positive definiteness for CSAREs solutions, feasible numerical algorithms that are based on Newtonôs method and the linear matrix inequality (LMI) for solving CSAREs is considered. Finally, the authors provide a numerical example to verify the efficiency of the proposed algorithms.