Geodesic
Solution of the differential game with hybrid structure
Contributions to game theory and management, Tome 12 (2019), pp. 159-176

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This paper focuses on two approaches for calculating optimal controls in cooperative differential games with hybrid structure: namely, the (joint) payoff function has a form of sum of integrals with different but adjoint time intervals. Our methods had been applied for the game-theoretical model with random time horizon $T$ where $T$ has a discrete structure. But the area of application can be more wide.
Keywords: differential games, random duration, discontinuous cumulative distribution function, discrete random variable, optimal control, Pontryagin's maximum principle. 
@article{CGTM_2019_12_a9,
     author = {Ekaterina V. Gromova and Natalya G. Magnitskaya},
     title = {Solution of the differential game with hybrid structure},
     journal = {Contributions to game theory and management},
     pages = {159--176},
     publisher = {mathdoc},
     volume = {12},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2019_12_a9/}
}
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Ekaterina V. Gromova; Natalya G. Magnitskaya. Solution of the differential game with hybrid structure. Contributions to game theory and management, Tome 12 (2019), pp. 159-176. http://geodesic.mathdoc.fr/item/CGTM_2019_12_a9/