A new approach for derivation of closed-loop stackelberg strategies

Abstract

This paper develops a new approach to obtain the closed-loop Stackelberg (CLS) solution of an important class of two-person nonzero-sum dynamic games characterized by linear state dynamics and quadratic cost functionals. The new technique makes use of an important property of nonunique representations of a closed-loop strategy, and it relates the CLS solution to a particular representation of the optimal solution of a team problem. This specific problem treated in this paper is a 3-stage Scalar LQ dynamic game, and within this context it is shown that the CLS strategies for the leader are linear and of the one-step memory type, while those of the follower can be realized in linear feedback form. Extensions of this solution to the general LQ dynamic two-person game are also discussed in the paper.