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Necessary conditions and sufficient conditions for pareto optimality in a multicriterion perturbed system

  • Jean-Louis Goffin
  • Alain Haurie
Game Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3)

Keywords

Cooperative Game Pareto Optimality Constraint Qualification Scalarization Process Side Payment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A.W. STARR et Y.C. HO: Nonzero-Sum Differential Games, JOTA, 3 (1969), 184–206.CrossRefGoogle Scholar
  2. [2]
    — Further Properties of Nonzero-Sum Differential Games, JOTA (1969), 207–219.Google Scholar
  3. [3]
    T.L. VINCENT & G. LEITMANN: Control Space Properties of cooperative games, JOTA, 4 (1970), 91–113.CrossRefGoogle Scholar
  4. [4]
    A. BLAQUIERE: Sur la géométrie des surfaces de Pareto d'un jeu différentiel à N joueurs, C.R. Acad. Sc. Paris Sér. A, 271 (1970), 744–747.Google Scholar
  5. [5]
    A. BLAQUIERE, L. JURICEK & K.E. WIESE: Sur la géométrie des surfaces de Pareto d'un jeu différentiel à N joueurs; théorème du maximum, C.R. Acad. Sc. Paris Sér. A, 271 (1970), 1030–1032.Google Scholar
  6. [6]
    A. HAURIE: Jeux quantitatifs à M joueurs, doctoral dissertation, Paris 1970.Google Scholar
  7. [7]
    M.C. DELFOUR & S.K. MITTER: Reachability of Perturbed Linear Systems and Min Sup Problems, SIAM J. On control, 7 (1969), 521–533CrossRefGoogle Scholar
  8. [8]
    D.P. BERTSEKAS & I.B. RHODES: On the Minimax Reachability of Targets and Target Tubes, Automatica, 7 (1971), 233–247.CrossRefGoogle Scholar
  9. [9]
    J.D. GLOVER & F.C. SCHWEPPE: Control of Linear Dynamic Systems with Set Constrained Disturbances, IEEE Trans. on Control, AC-16 (1971), 411–423.CrossRefGoogle Scholar
  10. [10]
    A. Haurie: On Pareto Optimal Decisions for a Coalition of a Subset of Players, IEEE Trans. on Automatic Control, avril 1973.Google Scholar
  11. [11]
    H.W. KUHN & A.W. TUCKER: Non-Linear Programming, 2nd Berkeley Symposium of Mathematical Statistics and Probability, Univ. Calif. Press, Berkeley 1951.Google Scholar
  12. [12]
    J. DANSKIN: On the Theory of Min-Max, J. SIAM Appl. Math., Vol. 14 (1966), pp. 641–664.CrossRefGoogle Scholar
  13. [13]
    V.F. DEM'YANOV & A.M. RUBINOV: Minimization of functionals in normed spaces, SIAM J. Control, Vol. 6 (1968), pp. 73–88.CrossRefGoogle Scholar
  14. [14]
    B. Lemaire: Problèmes min-max et applications au contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles linéaires, Thèse de doctorat, faculté des sciences, Université de Paris, 1970.Google Scholar
  15. [15]
    J. BRAM: The Lagrange Multiplier Theorem for Max-Min with several Constraints, J. SIAM App. Math. Vol 14 (1966), pp 665–667.CrossRefGoogle Scholar
  16. [16]
    R.J. Aumann: A Survey of Cooperative Games without side Payments, in Essays in Mathematical Economics, ed. M. Shubik, Princeton 1969.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • Jean-Louis Goffin
    • 1
  • Alain Haurie
    • 1
  1. 1.Ecole des Hautes Etudes CommercialesMontréal

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