Numerical Solution of Finite Time Nash Game for Stochastic Systems

Abstract

In this paper, a continuous-time, finite-time horizon Nash game for a class of stochastic systems is investigated. First, necessary condition attaining Nash equilibrium is derived by means of the existing stochastic optimal control policy. As a result, it is shown that the existence conditions consist of the cross-coupled forward-backward stochastic differential equations. Second, in order to obtain a strategy set, computational algorithm is discussed. In particular, four step scheme is adopted. Finally, simple examples are solved to show the validity of the proposed methodology.