Finite-horizon dynamic games for a class of nonlinear stochastic systems

This paper investigates finite-time horizon dynamic games for a class of nonlinear stochastic systems with multiple players. First, the necessary conditions for the existence of an open-loop Nash equilibrium are established using the stochastic maximum principle. Such conditions can be represented as the solvability conditions of cross-coupled forward-backward stochastic differential equations (CFBSDEs). Second, in order to obtain the open-loop Nash strategy set, a computational algorithm based on a four-step scheme is developed. As an alternative non-cooperative game, a Pareto-based Stackelberg game is also considered. Finally, a practical control example for reducing algal blooms in lake ecosystems is demonstrated to show the validity of the proposed method.