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Title: Nash and Stackelberg solutions to general linear-quadratic two player difference games. I. Open-loop and feedback strategies (English)
Author: Hämäläinen, Raimo P.
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 14
Issue: 1
Year: 1978
Pages: (38)-56
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Category: math
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MSC: 90D05
MSC: 91A20
MSC: 93C05
MSC: 93C55
idZBL: Zbl 0377.90103
idMR: MR0479419
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Date available: 2009-09-24T17:00:20Z
Last updated: 2012-06-05
Stable URL: http://hdl.handle.net/10338.dmlcz/125404
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Related article: http://dml.cz/handle/10338.dmlcz/125617
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Reference: [1] A. W. Starr Y., C. Ho: Nonzero-sum differential games.J. Optim. Theory. Applic. 3 (1969), 3, 184-206. Zbl 0169.12303, MR 0249117
Reference: [2] A. W. Starr Y., C. Ho: Further properties of nonzero-sum differential games.J. Optim. Theory. Applic. 3 (1969), 4, 207-219. Zbl 0169.12303, MR 0249118
Reference: [3] J. Marschak: Elements for a theory of teams.Management Science 1 (1955), 127-137. Zbl 0995.90544, MR 0075521
Reference: [4] R. Radner: Team decision problems.Ann. Math. Statistics 33 (1962), 857-881. Zbl 0217.57103, MR 0146937
Reference: [5] Y., C. Ho K., C. Chu: Team decision theory and information structures in optimal control problems - part I.IEEE Trans. Autom. Control AC-17 (1972), I, 15-22. MR 0359875
Reference: [6] K., C. Chu: Team decision theory and information structures in optimal control problems - part II.IEEE Trans. Autom. Control AC-17 (1972), 1, 22-28. MR 0359876
Reference: [7] R. Isaacs: Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization.John Wiley and Sens, New York 1965. Zbl 0125.38001, MR 0210469
Reference: [8] Y.-C. Ho A. E. Bryson Jr S. Baron: Differential games and optimal pursuit-evasion strategies.IEEE Trans Autom. Control AC-10 (1965), 4, 385-389. MR 0184747
Reference: [9] J. H. Case: Toward a theory of many player differential games.SIAM J. Control 7 (1969), 2, 179-197. Zbl 0176.39404, MR 0249111
Reference: [10] D. L. Lukes D. L. Russel: A global theory for linear-quadratic differential games.J. Math. Anal. Applic. 33 (1971), 96-123. MR 0269324
Reference: [11] N. J. Krikelis Z. V. Rekasius: On the solution of the optimal linear control problems under conflict of interest.IEEE Trans. Autom. Control AC-16 (1971), 2, 140-147. MR 0290810
Reference: [12] T. Basar: A counterexample in linear quadratic games: Existence of nonlinear Nash solutions.J. Optim. Theory. Applic. 14 (1974), 4, 425-430. MR 0456552
Reference: [13] T. Basar: Nash strategies for M-person differential games with mixed information structures.Automatica 11 (1975), 5, 547-551. Zbl 0318.90066, MR 0401190
Reference: [14] H. Stackelberg: Marktform und Gleichgewicht.Springer Verlag, Wien -Berlin 1934.
Reference: [15] C. I. Chen J. B. Cruz, Jr: Stackelberg solution for two-person games with biased information patterns.IEEE Trans. Autom. Control. AC-17 (1972), 6, 791-798.
Reference: [16] M. Simaan J. B. Cruz, Jr: On the Stackelberg strategy in nonzero-sum games.J. Optim. Theory. Applic. 11 (1973), 5, 533-555. MR 0332207
Reference: [17] M. Simaan J. B. Cruz, Jr: Additional aspects of the Stackelberg strategy in nonzero-sum games.J. Optim. Theory. Applic. 11 (1973), 6, 613-627. MR 0368809
Reference: [18] M. Simaan J. B. Cruz, Jr: Sampled-data Nash controls in non-zero-sum differential games.Int. J. Control 77 (1973), 6, 1201-1209. MR 0327317
Reference: [19] M. Simaan J. B. Cruz, Jr: A Stackelberg solution for games with many players.IEEE Trans. Autom. Control. AC-18 (1973), 3, 322-324. MR 0441373
Reference: [20] Y. Nishikawa H. Itakura H. Kitagawa: Nonzero-sum differential games with nonlinear dynamics.Institute of Electronics and Communication Engineers of Japan, Tokyo. Report NLP 71-18, 1972.
Reference: [21] L. F. Pau: Differential games and a Nash equilibrium searching algorithm.SIAM J. Control 75 (1975), 4, 835-852. Zbl 0269.90062, MR 0386720
Reference: [22] R. Mukundan W. B. Eisner: Linear feedback strategies in non-zero-sum differential games.Int. J. Systems Sci. 6 (1975), 6, 513-532. MR 0371427
Reference: [23] J. Doležal: Necessary optimality conditions forN-player nonzero-sum multistage games.Kybernetika 12 (1976), 4, 268-295. MR 0429152
Reference: [24] J. Doležal: Hierarchical solution concepts for static and multistage decision problems with two objectives.Kybernetika 12 (1976), 5, 363 - 385. MR 0449468
Reference: [25] R. P. Hämäläinen: Nash and Stackelberg solutions to general linear-quadratic two-player difference games. Part II. Open-closed strategies.Kybernetika, 14 (1978), to appear. MR 0479420
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