Abstract
The general nonzero-sum differential game hasN players, each controlling a different set of inputs to a single nonlinear dynamic system and each trying to minimize a different performance criterion. These general games have several interesting features which are absent in the two bestknown 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 theprinciple of optimality and the relation betweenopen-loop andclosed-loop controls. Two types of solutions are discussed: theNash equilibrium and thenoninferior set. Some simple multistage discrete games are used to illustrate phenomena which also arise in the continuous formulation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Starr, A. W., andHo, Y. C.,Nonzero-Sum Differential Games, Journal of Optimization Theory and Applications, Vol. 3, No. 3, 1969.
Case, J. H.,Equilibrium Points of N-Person Differential Games, University of Michigan, Department of Industrial Engineering, TR No. 1967-1, 1967.
Isaacs, R.,Differential Games, John Wiley and Sons, New York, 1965.
Dacunha, N. O., andPolak, E.,Constrained Minimization Under Vector-Valued Criteria in Finite-Dimensional Spaces, University of California at Berkeley, Electronics Research Laboratory, Memorandum No. ERL-M188, 1966.
Author information
Authors and Affiliations
Additional information
This research was supported by Joint Services Electronics Contracts Nos. N00014-67-A-0298-0006, 0005, 0008 and by NASA Grant No. NGR 22-007-068.
Rights and permissions
About this article
Cite this article
Starr, A.W., Ho, Y.C. Further properties of nonzero-sum differential games. J Optim Theory Appl 3, 207–219 (1969). https://doi.org/10.1007/BF00926523
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00926523