Stochastic Nash games with state-dependent noise

Abstract

This paper discusses the infinite horizon stochastic Nash games with state-dependent noise. First, stochastic Nash games are formulated by applying the results of stochastic linear quadratic control problems. Second, in order to obtain the Nash strategy, cross-coupled stochastic algebraic Riccati equations (CSAREs) are derived. Moreover, the algorithm that is based on the Newton's method is considered for solving the CSAREs. In order to demonstrate the efficiency of the proposed algorithms, computational examples are provided.