Abstract
The paper is concerned with a two-player nonzero-sum differential game in the case when players are informed about the current position. We consider the game in control with guide strategies first proposed by Krasovskii and Subbotin. The construction of universal strategies is given both for the case of continuous and discontinuous value functions. The existence of a discontinuous value function is established. The continuous value function does not exist in the general case. In addition, we show the example of smooth value function not being a solution of the system of the Hamilton–Jacobi equation.
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Acknowledgments
The work was supported by RFBR (grant nos. 12-01-00537) and Presidium of RAS (program ‘Mathematical Control Theory’, project UrB RAS N12-P-1-1019).
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Averboukh, Y. Universal Nash Equilibrium Strategies for Differential Games. J Dyn Control Syst 21, 329–350 (2015). https://doi.org/10.1007/s10883-014-9224-9
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DOI: https://doi.org/10.1007/s10883-014-9224-9