Abstract
We propose a discretization scheme for an undiscounted zero sum differential game with stopping times. The value function of the original problem satisfies an integral inequality of Isaacs type that we can discretize using finite difference or finite element techniques.
The fully discrete problem defines a stochastic game problem associated with the process, which may have, in general, multiple solutions. Among these solutions there exists one which is naturally associated with the value function of the original problem.
The main contribution of this paper is the complete characterization of the set of solutions and the description of a procedure to identify the desired solution. We also present accelerated algorithms in order to efficiently compute the discrete solution.
This work was partially done during a visit of the author at INRIA - Sophia Antipolis, France
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Tidball, M.M. (1995). Undiscounted Zero Sum Differential Games with Stopping Times. In: Olsder, G.J. (eds) New Trends in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 3. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4274-1_15
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DOI: https://doi.org/10.1007/978-1-4612-4274-1_15
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8719-3
Online ISBN: 978-1-4612-4274-1
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