Comparison of Two Numerical Approaches for the Barrier and Value of a Simple Pursuit—Evasion Game

  • Pierre Bernhard
  • Stephane Crepey
  • Alain Rapaport
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 6)


We investigate the barrier of a simple pursuit—evasion game for which we are able to compare two theoretical and numerical approaches. One is based directly on the capture time, and the second one, introduced by one of the authors, transforms the game in one of approach (or L -criterion). This second approach gives both a new characterization of barriers and a new, potentially more robust, numerical method for the determination of barriers. We provide a detailed analytical solution of the various problems thus raised and use it as a benchmark for the numerical method.


Variational Inequality Viscosity Solution Differential Game Stochastic Game Feedback Strategy 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Pierre Bernhard
    • 1
    • 2
  • Stephane Crepey
    • 3
  • Alain Rapaport
    • 4
  1. 1.University of NiceFrance
  2. 2.I3S CNRS-UNSASophia AntipolisFrance
  3. 3.INRIASophia AntipolisFrance
  4. 4.INRIAMontpelierFrance

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