弱結合大規模マルコフジャンプ確率システムのためのナッシュゲーム

Abstract

In this paper, the stochastic Nash games for stochastic Markov jump systems are investigated. First, the Nash equilibrium is defined and the existence conditions are formulated. In particular, necessary and sufficient conditions for the existence of two cross-coupled stochastic algebraic Riccati equations (CSAREs) are developed. Moreover, in order to obtain the required solutions, a numerical algorithm that is based on the Newton's method is proposed. As an important implication, weakly-coupled large-scale systems are also adopted. After establishing the asymptotic structure of the solutions for the CSAREs, the quadratic convergence result that is based on the Newton's method is shown. Finally, a numerical example is given to demonstrate the availability of the proposed method.