This book deals with the theory and applications of noncooperative differential games. A noncooperative game is a strategic situation in which decision makers (from now on: players) cannot make binding agreements to cooperate. In a noncooperative game, the players act independently in the pursuit of their own best interests. Confining our interest to noncooperative games should not be seen as an indication that cooperative games are less interesting. The reason simply is that, in the area of differential games, cooperative theory is far less developed than noncooperative theory and almost all applications in economics and management science are in the noncooperative setup. We do not deal with zero-sum games (these are games in which the players have completely opposite interests, that is, the gain for one player equals the loss for another player), because the zero-sum assumption is only plausible in rather special situations in economics and management science.

Differential games belong to a subclass of dynamic games called state space games. In a state space game, the modeller introduces a set of (state) variables to describe the state of a dynamic system at any particular instant during play. The hypothesis is that the payoff-relevant influence of past events is adequately summarized in the state variables. To illustrate, the state vector may consist of the current capital stocks of N oligopolistic firms and these stocks can be influenced by the firms through the choices of their individual investment rates.