Nonlinear Elliptic Systems Arising from Stochastic Games

  • Alain Bensoussan
  • Jens Frehse
Part of the Applied Mathematical Sciences book series (AMS, volume 151)


The objective of this section is to present some results concerning a class of stochastic games for N players, obtained from the study of nonlinear elliptic systems, the Bellman system. The method consists in applying the dynamic programming approach. The value functions are the solutions of a system of partial differential equations. From regularity results, one is able to construct continuous feedbacks, which will represent optimal controls for each player. The standard verification approach will show the optimality. The optimality is to be taken in the sense of Nash [82]; see also J.P. Aubin [3].


Weak Solution Maximum Principle Linear Transformation Coupling Term Smallness Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alain Bensoussan
    • 1
  • Jens Frehse
    • 2
  1. 1.CNESParisFrance
  2. 2.Institut für Angewandte MathematikUniversität BonnBonnGermany

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