Abstract
The generalized viscosity solution of the basic (Bellman-Isaacs) equation in dynamic game theory is considered [1]. An assumptiom is made that the solution (game value) is nonsmooth on some hypersurface. Local necessary conditions in the form of equalities and inequalities are obtained for viscosity solution under different assumptions about the behaviour of the optimal paths in the vicinity of singular surface. The singular surfaces are investigated, which contain (as equivocal or focal ones) or not (dispersal one) the optimal singular paths [2,3]. Using the equality-conditions and singular charactristics technique [4] the equations of motion for the former surfaces are obtained. These equations appear to be not of Hamiltonian type but more general. Some results of this paper are obtained using other approaches in [4,5]; their connection with the properties of viscosity solutions is stated here.
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© 1994 Springer Science+Business Media New York
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Melikyan, A.A. (1994). Singular Paths in Differential Games with Simple Motion. In: Başar, T., Haurie, A. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 1. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0245-5_7
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DOI: https://doi.org/10.1007/978-1-4612-0245-5_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6679-2
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