Nonclassical Control Problems and Stackelberg Games 155

H IERARCHICAL and large scale systems have received considerable attention during the last few years; firstly because of their importance in engineering, economics, and other areas, and secondly because of the increased capability of computer facilities [13], [14]. An important characteristic of many large scale systems is the presence of many decision makers with different and usually conflicting goals. The existence of many decision makers who interact through the system and have different goals may be an inherent property of the system under consideration (e.g., a market situation), or may be simply the result of modeling the system as such (e.g., a large system decomposed to subsystems for calculation purposes). Differential games are useful in modeling and studying dynamic systems where more than one decision maker is involved. Most of the questions posed in the area of the classical control problem may be considered in a game situation, but their esolution is generally more difficult. In addition, many questions can be posed in a game framework, which are meaningless or trivial in a classical control problem framework. The superior conceptual wealth of game over control problems, which makes them potentially much more applicable, counterbalances the additional difficulties encountered in their solution. A particular class of games are the so-called Stackelberg differential games [ 11-[SI. Stackelberg games provide a natural formalism for describing systems which operate on many different levels with a corresponding hierarchy of decisions. The mathematical definition of a general