Abstract
We consider the class of differential games with random duration. We show that a problem with random game duration can be reduced to a standard problem with an infinite time horizon. A Hamilton-Jacobi-Bellman-type equation is derived for finding optimal solutions in differential games with random duration. Results are illustrated by an example of a game-theoretic model of nonrenewable resource extraction. The problem is analyzed under the assumption of Weibull-distributed random terminal time of the game.
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Original Russian Text © E.V. Shevkoplyas, 2009, published in Matematicheskaya Teoriya Igr i Prilozheniya, 2009, No. 2, pp. 98–118.
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Shevkoplyas, E.V. The Hamilton-Jacobi-Bellman equation for a class of differential games with random duration. Autom Remote Control 75, 959–970 (2014). https://doi.org/10.1134/S0005117914050142
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DOI: https://doi.org/10.1134/S0005117914050142