Linear-Quadratic Gaussian dynamic games with a control-sharing information pattern

Abstract

A “zero-sum” Linear-Quadratic Gaussian Dynamic Game (LQGDG) where the players have partial information is considered. Specifically, the players’ initial state information and their measurements are private information, but each player is able to observe his antagonist’s past inputs: the protagonists’ past controls is shared information. Although this is a game with partial information, the control-sharing information pattern renders the game amenable to solution by the method of dynamic programming. The correct solution of LQGDGs with a control-sharing information pattern is obtained in closed-form.