Differential games: Their scope, nature, and future

Abstract

There is a profound distinction between classical mathematical analysis and game theory which comes into especial prominence with the advent of differential games. There is a hierarchy of theories of applied mathematics in which the classical theory is the bottom row. Thus, it is important in the inevitable pending developments of higher forms of game theory to be prepared for ideas and concepts which break with tradition. These general thoughts, not at present widely understood, are expounded here with some simple examples which already illustrate the novelties of future research.