The Role of Information in Nonzero-Sum Differential Games

Abstract

Games are an ideal vehicle for showcasing the crucial role information plays in decision systems. Indeed, game theory plays a major role in economic theory, and, in particular, in microeconomic theory—one aptly refers to information economics. The role of information is further amplified in dynamic games. One then refers to the information pattern of the game. In this paper nonzero-sum differential games are addressed and open-loop and state feedback information patterns are considered. Nash equilibria (NE) when complete state information is available and feedback strategies are sought are compared to open-loop NE. In contrast to optimal control and, remarkably, zero-sum differential games, in nonzero-sum differential games the optimal trajectory and the players’ values when closed-loop strategies are used are not the same as when open-loop strategies are used. This is amply illustrated in the special case of nonzero-sum Linear-Quadratic differential games. Results which quantify the cost of uncertainty are derived and insight into the dynamics of information systems is obtained.