ON SOME FURTHER PROPERTIES OF NONZERO-SUM DIFFERENTIAL GAMES.
HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
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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
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