Chapter 1 Introduction and Motivation

Abstract

Publisher SummaryThis chapter introduces the dynamic noncooperative game theory. Game theory involves multiperson decision-making; it is dynamic if the order in which the decisions are made is important, and it is noncooperative if each person involved pursues his or her own interests, which are partly conflicting with others. The applications of game theory and the theory of differential games mainly deal with economic and political conflicting situations, worst-case designs, and also modeling of war games. However, it is not only the applications in these fields that are important; equally important is the development of suitable concepts to describe and understand conflicting situations. It turns out, for instance, that the role of information—what one player knows relative to others—is very crucial in such problems. Scientifically, dynamic game theory can be viewed as a child of the parent game theory and optimal control theory. Its character, however, is much more versatile than that of either of its parents, because it involves a dynamic decision process evolving in (discrete or continuous) time with more than one decision maker, each with his own cost function and possibly having access to different information. This view is the starting point behind the formulation of games in extensive form.