Incentive stackelberg strategies in linear quadratic differential games with two noncooperative followers

Abstract

This paper is mainly concerned with the derivation of the sufficient conditions for the incentive Stackelberg strategy in the two-level hierarchical differential games with two noncooperative followers, characterized by a classof linear state dynamics and quadratic cost functionals. In the paper, we first give some concepts in the two-level hierarchical games with two noncooperative followers, and by a simple numerical example, show a general method of solving such a two-level incentive static game problem. Then, we construct a new form of the incentive Stackelberg strategy $\bar \gamma _0 = \left\{ {\bar \gamma _{0 1} ,\bar \gamma _{0 2} } \right\}$ of the leader P0, and also derive the sufficient conditions which are satisfied by this strategy $\bar \gamma _0 = \left\{ {\bar \gamma _{0 1} ,\bar \gamma _{0 2} } \right\}$.