Abstract
Cooperative differential games having convex control sets are investigated. Two criteria are given for the utility of analyzing Pareto-optimal solutions of such games. The criteria are shown to determine whether a Pareto-optimal control policy belongs to the boundary of the control set or to the interior. A condition which is necessary for Pareto-optimality in such games is employed to obtain the results. An example is given to demonstrate that the results do not necessarily apply to games having nonconvex control sets.
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Vincent, T. L., andLeitmann, G.,Control-Space Properties of Cooperative Games, Journal of Optimization Theory and Applications, Vol. 6, No. 2, 1970.
Basile, G., andVincent, T. L.,On the Cooperative Differential Game, Paper presented at the Third Hawaii International Conference on System Sciences, Honolulu, Hawaii, 1970.
Sandgren, L.,On Convex Cones, Mathematica Scandinavica, Vol. 2, 1954.
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Communicated by G. Leitmann
Fruitful discussion on the subject matter with Professor G. Leitmann, University of California, Berkeley, California, is gratefully acknowledged, as is secretarial assistance from Miss Kathy Murphy.
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Stalford, H.L. Criteria for Pareto-optimality in cooperative differential games. J Optim Theory Appl 9, 391–398 (1972). https://doi.org/10.1007/BF00934739
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DOI: https://doi.org/10.1007/BF00934739