Multilevel Dynamic Games

Von Neumann and Morgenstern [1] were the first to use modern mathematics for constructing a fairly complete theory describing conflict-type situations. This led to a new and still rapidly developing branch of mathematics, namely the theory of games. In a conflict situation we have the participation of several active sides with different interests, able to select their actions from a set of possible alternatives. The participants thus have some influence on the course of events, without being able to exercise complete control over them. Recently, however, a new and more general point of view has received currency [2], whereby game theory is treated as a theory of decision making under uncertainty. On the other hand, many applications of the theory of games do not deal with conflicts as such, but with processes that are only interpreted as conflicts. Among processes to which game theory has been applied in this sense is operations research, economics, problems of production control, and social sciences.