Abstract
In this paper we will present a brief sketch of how the leader-follower or Stackelberg strategy concept for two-person dynamic nonzero-sum games might be extended to the coordination of several subsystems. We will also explore how hierarchical control could be formulated in the Stackelberg sense.
This work was supported in part by the National Science Foundation under Grant GK-36276, in part by the Joint Services Electronics Program under Contract DAAB-07-72-C-0259, and in part by the U.S. Air Force under Grant AFOSR-73-2570.
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References
Y. C. Ho, “Commentator’s Report on Session on Differential Games,” Proc. of the Fifth World Congress of IFAC, Paris, 1972.
Y. C. Ho, “Decisions, Control, and Extensive Games,” Proc. of the Sixth World Congress of IFAC, Boston, 1975.
J. H. Case, “Toward a Theory of Many Player Differential Games, ” SIAM Journal on Control, Vol. 7, 1969, pp. 179–197.
H. von Stackelberg, The Theory of the Market Economy, Oxford University Press, Oxford, England, 1952.
C. I. Chen and J. B. Cruz, Jr., “Stackelberg Solution for Two-Person Games with Biased Information Patterns,” IEEE Trans, on Automatic Control, Vol. AC-17, No. 5, 1972, pp. 791–798.
M. Simaan and J. B. Cruz, Jr., “On the Stackelberg Strategy in Nonzero-Sum Games,” Journal of Optimization Theory and Applications, Vol. 11, No. 5, 1973, pp. 533–555.
M. Simaan and J. B. Cruz, Jr., “Additional Aspects of the Stackelberg Strategy in Nonzero-Sum Games,” Journal of Optimization Theory and Applications, Vol. 11, No. 6, 1973, pp. 613–626.
M. Simaan and J. B. Cruz, Jr., “A Stackelberg Strategy for Games with Many Players,” IEEE Trans, on Automatic Control, Vol. AC-18, No. 3, 1973, pp. 322–324.
T. Basar, “On the Relative Leadership Property of Stackelberg Strategies,” Journal of Optimization Theory and Applications, Vol. 11, No. 6, 1973, pp. 655–661.
J. B. Cruz, Jr., “Survey of Nash and Stackelberg Equilibrium Strategies in Dynamic Games, ” Annals of Economic and Social Measurement, Vol. 4, No. 2, 1975, pp. 339–344.
D. Castanon and M. Äthans, “On Stochastic Dynamic Stackelberg Strategies,” Proc. Sixth World Congress of IFAC, Boston, 1975.
P. V. Kokotovic, R. E. O’Malley and P. Sannuti, “Singular Perturbations and Order Reduction in Control Theory-An Overview,” Proc. Sixth World Congress of IFAC, 1975, Boston.
P. V. Kokotovic, “Feedback Design of Large Linear Systems,” Chapter 4 in Feedback Systems, J. B. Cruz, Jr., editor, McGraw-Hill Book Co., New York, 1972, pp. 99–137.
P. V. Kokotovic, W. R. Perkins, J. B. Cruz, Jr., and G. D’Ans, “e-Coupling Method for Near Optimum Design of Large Scale Linear Systems,” Proc. IEE, Vol. 116, pp. 889–892, 1969. Also in System Sensitivity Analysis, J. B. Cruz, Jr., editor, Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1973, pp. 313–316.
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© 1976 Plenum Press, New York
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Cruz, J.B. (1976). Stackelberg Strategies for Multilevel Systems. In: Ho, Y.C., Mitter, S.K. (eds) Directions in Large-Scale Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2259-7_10
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DOI: https://doi.org/10.1007/978-1-4684-2259-7_10
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