Convergence of adaptive linear stochastic differential games: Nonzero-sum case

Abstract

Complex systems with components or subsystems having game-like relationships are probably the most complex ones that we encounter everyday. Much progress has been made over the past half century on differential games which are used as a tool in modeling conflicts in the context of dynamic systems, however, almost all of the current literature assume that both the parameters and the structure of the game are known to the players. Since in many practical situations, the players may have unknown parameters, which motivate us to investigate a class of two-player zero-sum linear-quadratic stochastic differential games in [1] with unknown parameters. In this paper, we will further consider a class of two-player nonzero-sum linear quadratic stochastic differential games, with unknown parameters to both players. We will design adaptive strategies and prove that they will converge to the optimal ones under some natural conditions on the true parameters of the system.