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Journal of Optimization Theory and Applications

, Volume 26, Issue 4, pp 637–643 | Cite as

On generalized Stackelberg strategies

  • G. Leitmann
Technical Note

Abstract

The concept of Stackelberg strategy for a nonzero-sum two-person game is extended to allow for a nonunique “rational” response of the follower. This leads to the notion of a generalized Stackelberg strategy for the leader, which guarantees him a cost value that cannot be exceeded, no matter what the “rational” response of the follower. Then, a generalized Stackelberg strategy pair is defined. A simple example is given. The idea of a generalized Stackelberg strategy and strategy pair is then applied to the situation of one leader and many “rational” followers.

Key Words

Stackelberg strategies nonzero-sum games leader-follower decision making 

References

  1. 1.
    Von Stackelberg H.,The Theory of the Market Economy, Oxford University Press, Oxford, England, 1952.Google Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    Nash, J. F.,Non-Cooperative Games, Annals of Mathematics, Vol. 54, No. 2, 1951.Google Scholar
  4. 4.
    Leitmann, G.,Cooperative and Non-Cooperative Many Player Differential Games, CISM Monograph No. 190, Springer-Verlag, Vienna, Austria, 1974.Google Scholar
  5. 5.
    Leitmann, G., andMarzollo, A.,Multicriteria Decision Making, CISM Monograph No. 211, Springer-Verlag, Vienna, Austria, 1975.Google Scholar
  6. 6.
    Pareto, V.,Manuel d'Economique Politique, Girard et Briere, Paris, France, 1909.Google Scholar
  7. 7.
    Yu, P. L., andLeitmann, G.,Nondominated Decisions and Cone Convexity in Dynamic Multicriteria Problems, Journal of Optimization Theory and Applications, Vol. 14, No. 5, 1974.Google Scholar

Additional Bibliography

  1. 8.
    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.Google Scholar
  2. 9.
    Chen, S. F. H.,Labor-Management Bargaining: A Differential Game, Doctoral Dissertation, University of California, Berkeley, 1976.Google Scholar
  3. 10.
    Gardner, B. F., Jr., andCruz, J. B., Jr.,Feedback Stackelberg Strategy for a Two-Player Game, IEEE Transactions on Automatic Control, Vol. AC-22, No. 2, 1977.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • G. Leitmann
    • 1
  1. 1.University of CaliforniaBerkeley

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