Nash and Stackelberg solutions to general linear-quadratic two-player difference games. II. Open-closed strategies

This paper deals with difference games in which the information structures of the players are not equal. Nash and Stackelberg solutions to deterministic linear-quadratic two-player difference games are presented. The open-closed strategies are considered where one of the players can only use the initial state whereas the other has access to perfect memory information of the state. Stackelberg open-closed strategies are treated only in the case where the leader has access to open-loop information. A combined dynamic programming and augmentation techniques approach is developed. A computationally straightforward recursive algorithm is derived for the Nash open-closed solution.