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Multilevel Stackelberg strategies in linear-quadratic systems

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Abstract

Open-loop multilevel Stackelberg strategies in deterministic, sequential decision-making problems for continuous linear systems and quadratic criteria are developed. Characterization of the Stackelberg controls via the solution of a higher-order square-matrix-Riccati differential equation is established; also, the basic structural properties of the coefficient matrices of this differential equation are established, and the basic structural properties of its solution are inferred.

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References

  1. Von Stackelberg, H.,The Theory of the Market Economy, Oxford University Press, Oxford, England, 1952.

    Google Scholar 

  2. Chen, C. I., andCruz, J. B., Jr.,Stackelberg Solution for Two-Person Games with Biased Information Patterns, IEEE Transactions on Automatic Control, Vol. AC-17, No. 6, 1972.

  3. Simaan, M., andCruz, J. B., Jr.,On the Stackelberg Strategy in Nonzero-Sum Games, Journal of Optimization Theory and Applications, Vol. 11, No. 5, 1973.

  4. Cruz, J. B., Jr.,Survey of Nash and Stackelberg Equilibrium Strategies in Dynamic Games, Annals of Economic and Social Measurement, Vol. 4, No. 2, 1975.

  5. Simaan, M., andCruz, J. B., Jr.,Additional Aspects of the Stackelberg Strategy in Nonzero-Sum Games, Journal of Optimization Theory and Applications, Vol. 11, No. 6, 1973.

  6. Basar, T.,On the Relative Leadership Property of Stackelberg Strategies, Journal of Optimization Theory and Applications, Vol. 11, No. 6, 1973.

  7. Castanon, D., andAthans, M.,On the Stochastic Dynamic Stackelberg Strategies, Proceedings of the 6th World Congress of the International Federation of Automatic Control, Boston, Massachusetts, 1975.

  8. Cruz, J. B., Jr.,Stackelberg Strategies for Multilevel Systems, Directions in Large-Scale Systems, Edited by Y. C. Ho and S. K. Mitter, Plenum Press, New York, New York, 1975.

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Author information

Authors and Affiliations

  1. Coordinated Science Laboratory, University of Illinois, Urbana, Illinois

    J. Medanic (Visiting Research Associate Professor)

  2. Mihailo Pupin Institute, Belgrade, Yugoslavia

    D. Radojevic (Research Associate)

Authors
  1. J. Medanic
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  2. D. Radojevic
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Additional information

Communicated by G. Leitmann

This work was supported in part by the Energy Research and Development Administration, Contract No. ERDA E(49-18)-2088.

on leave from the Mihailo Pupin Institute, Belgrade, Yugoslavia.

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Medanic, J., Radojevic, D. Multilevel Stackelberg strategies in linear-quadratic systems. J Optim Theory Appl 24, 485–497 (1978). https://doi.org/10.1007/BF00932891

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  • DOI: https://doi.org/10.1007/BF00932891

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