A Non Cooperative Game in a Distributed Parameter System

  • J. P. Yvon
Part of the Lecture Notes in Computer Science book series (LNCIS)


This paper is devoted to study a class of differential games for distributed parameter systems. Essentially we study a Nash equilibrium point for a system governed by a parabolic equation. A method based on the SCARF-HANSEN [1] algorithm for solution of non-cooperative games is given.


Nash NASH 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. BENSOUSSAN “Point de Nash pour des jeux différentiels à n personnes”. To appear in SIAM J. of Control.Google Scholar
  2. [1]
    A. BENSOUSSAN, J.L. LIONS, R. TEMAM Cahier de l’IRIA n°11. June 1972.Google Scholar
  3. [1]
    J.D. BREDEHOEFT, R. YOUNG “The temporal allocation of a ground-water a simulation approach”. Water Resource Research. Vol. 6 n°1. (1970)Google Scholar
  4. [1]
    B.C. EAVES “Computing Kakutani fixed points” Siam J. of Appl. Math. Vol. 21 n° 2 (1971).Google Scholar
  5. [1]
    T. HANSEN, H. SCARF “On the approximation of a Nash equil.point” Cowles Foundation. Discussion paper n°272.Google Scholar
  6. [1]
    H.W. KUHN “Simplicial approximation of fixed points”. Proc. N.A.S. n°6 (1968).Google Scholar
  7. [1]
    J.L. LIONS Contrôle optimal des systèmes distribués. DUNOD (1968).Google Scholar
  8. [2]
    J.L. LIONS Quelques méthodes de résolution des problèmes non linéaires. DUNOD Paris (1969).MATHGoogle Scholar
  9. [1]
    J. NASH “Equilibrium points in N person game”. Proc. of N.A.A. Vol. 36 (1950).Google Scholar
  10. [1]
    J.B. ROSEN “Existence and uniqueness of Equilibrium point for concave n-person game”. Econometrica Vol. 33 n°3 (1965).Google Scholar
  11. [1]
    H. SCARF 16 “The approx. of fixed points...”. SIAM J. of App. Math. Vol. 15 n°5 (1967).Google Scholar
  12. [1]
    J.P. YVON To appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • J. P. Yvon
    • 1
  1. 1.Iria - Laboria73 - RocquencourtFrance

Personalised recommendations