Abstract
We describe an approximation scheme for the value function of general pursuit-evasion games and prove its convergence, in a suitable sense. The result works for problems with discontinuous value function as well, and it is new even for the case of a single player. We use some very recent results on generalized (viscosity) solutions of the Dirichlet boundary value problem associated to the Isaacs equation, and a suitable variant of Fleming’s notion of value. We test the algorithm on some examples of games in the plane.
Partially supported by M.U.R.S.T., project “Problemi nonlineari nell’analisi e nelle applicazioni fisiche, chimiche e biologiche”.
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Bardi, M., Bottacin, S., Falcone, M. (1995). Convergence of Discrete Schemes for Discontinuous Value Functions of Pursuit-Evasion Games. 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_14
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DOI: https://doi.org/10.1007/978-1-4612-4274-1_14
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