Abstract
In ak-player, nonzero-sum differential game, there exists the possibility that a group of players will form a coalition and work together. If allk players form the coalition, the criterion usually chosen is Pareto optimality whereas, if the coalition consists of only one player, a minmax or Nash equilibrium solution is sought.
In this paper, games with coalitions of more than one but less thank players are considered. Coalitive Pareto optimality is chosen as the criterion. Sufficient conditions are presented for coalitive Pareto-optimal solutions, and the results are illustrated with an example.
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References
Schmitendorf, W. E.,Differential Games Without Pure Strategy Saddle Point Solutions, Journal of Optimization Theory and Applications, Vol. 18, No. 1, 1976.
Starr, A. W., andHo, Y. C.,Further Properties of Nonzero-Sum Differential Games, Journal of Optimization Theory and Applications, Vol. 3, No. 4, 1969.
Schmitendorf, W. E., andFoley, M. H.,On a Class of Nonzero-Sum, Linear-Quadratic Differential Games, Journal of Optimization Theory and Applications, Vol. 7, No. 5, 1971.
Starr, A. W., andHo, Y. C.,Nonzero-Sum Differential Games, Journal of Optimization Theory and Applications, Vol. 3, No. 3, 1969.
Da Cunha, N. O., andPolak, E.,Constrained Minimization Under Vector-Valued Criteria in Linear Topological Spaces, Mathematical Techniques of Optimization, Academic Press, New York, New York, 1967.
Vincent, T. L., andLeitmann, G.,Control Space Properties of Cooperative Games, Journal of Optimization Theory and Applications, Vol. 9, No. 5, 1972.
Leitmann, G., Rocklin, S., andVincent, T. L.,A Note on Control Space Properties of Cooperative Games, Journal of Optimization Theory and Applications, Vol. 9, No. 6, 1972.
Leitmann, G., andSchmitendorf, W. E.,Some Sufficiency Conditions for Pareto-Optimal Control, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 95, No. 4, 1973.
Schmitendorf, W. E., andLeitmann, G.,A Simple Derivation of Necessary Conditions for Pareto Optimality, IEEE Transactions on Automatic Control, Vol. AC-19, No. 5, 1974.
Haurie, A.,On Pareto-Optimal Decisions for Coalition of a Subset of Players, IEEE Transactions on Automatic Control, Vol. AC-18, No. 2, April 1973.
Rekasius, Z. V.,On Closed-Loop and Open-Loop Solutions of Differential Games, Paper presented at the Purdue Centennial Symposium on Information Processing, Lafayette, Indiana, 1969.
Schmitendorf, W. E.,Existence of Optimal Open-Loop Strategies for a Class of Differential Games, Journal of Optimization Theory and Applications, Vol. 5, No. 5, 1970.
Friedman, A.,Differential Games, John Wiley and Sons (Interscience Publishers), New York, New York, 1971.
Leitmann, G.,Sufficiency Theorems for Optimal Control, Journal of Optimization Theory and Applications, Vol. 2, No. 5, 1968.
Stalford, H.,Sufficient Conditions for Optimal Controls with State and Control Constraints, Journal of Optimization Theory and Applications, Vol. 7, No. 2, 1971.
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Communicated by G. Leitmann
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Schmitendorf, W.E., Moriarty, G. A sufficiency condition for coalitive pareto-optimal solutions. J Optim Theory Appl 18, 93–102 (1976). https://doi.org/10.1007/BF00933797
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DOI: https://doi.org/10.1007/BF00933797