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Nash equilibria in nonzero-sum differential games with impulse control
Date Issued
01-12-2021
Author(s)
Abstract
In this paper, we introduce a class of deterministic finite-horizon two-player nonzero-sum differential games where one player uses ordinary controls while the other player uses impulse controls. We use the word ‘ordinary’ to mean that Player 1 uses control strategies that are piecewise continuous functions of time. We formulate the necessary and sufficient conditions for the existence of an open-loop Nash equilibrium for this class of differential games. We specialize these results to linear-quadratic games, and show that the open-loop Nash equilibrium strategies can be computed by solving a constrained non-linear optimization problem. In particular, for the impulse player, the equilibrium timing and level of impulses can be obtained. Furthermore, for the special case of linear-state differential games, we obtain analytical characterization of equilibrium number, timing, and the level of impulse in terms of the problem data. We illustrate our results using numerical experiments.
Volume
295