On non-standard Isaac’s wall pursuit game using dynamic programming method

Aicha Ghanem, Touffik Bouremani, Djamel Benterki and Abderrahmane Ziad ()
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Aicha Ghanem: UFAS1 - Université Ferhat-Abbas Sétif 1 [Sétif]
Touffik Bouremani: UFAS1 - Université Ferhat-Abbas Sétif 1 [Sétif]
Djamel Benterki: UFAS1 - Université Ferhat-Abbas Sétif 1 [Sétif]
Abderrahmane Ziad: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique

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Abstract: The present paper investigates the perpetual dilemma in the wall pursuit game in a non-standard form, which was proposed as an unsolved problem in Mirică 2004. The fundamental aspect of our approach involves using a novel variant of dynamic programming, which incorporates some refinements of Cauchy's method of characteristics for the stratified Hamilton-Jacobi equations. This, in turn, allows us to aggregate all the admissible trajectories in the form of maximal flows. Consequently, we identify a certain value function that proves useful in checking the optimality of an admissible pair of feedback strategies, through one of the verification theorems for locally Lipschitz functions as sufficient optimality conditions. The results of our study are consolidated by numerical representations that correspond to our theoretical purpose.

Keywords: Verification theorems; Hamiltonian flow; Feedback strategies; Pursuit-evasion games; Dynamic programming; Differential games (search for similar items in EconPapers)
Date: 2026
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Published in Journal of Computational and Applied Mathematics, 2026, 487, pp.117701. ⟨10.1016/j.cam.2026.117701⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05619142

DOI: 10.1016/j.cam.2026.117701

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