On Some Further Properties of Nonzero-Sum Differential Games

摘要

The general nonzero-sum differential game has N players, each controlling a different set of inputs to a single nonlinear dynamic system and each trying to minimize a different performance criterion. Several interesting new phenomena arise in these general games which are absent in the two best-known special cases (the optimal control problem and the two person zero-sum differential game). This paper considers some of the difficulties which arise in attempting to generalize ideas which are well-known in optimal control theory, such as the 'principle of optimality' and the relation between 'open-loop' and 'closed-loop' controls. Two types of 'solutions' are discussed: the 'Nash equilibrium' and the 'noninferior set.' Some simple multistage discrete (bimatrix) games are used to illustrate phenomena which also arise in the continuous formulation. (Author)