Geodesic
Nash and Stackelberg Solutions Numerical Construction in a Two-Person Nonantagonistic Linear Positional Differential Game
Contributions to game theory and management, Tome 2 (2009), pp. 205-219

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The paper suggests numerical methods for constructing Nash and Stackelberg solutions in a linear two-person positional differential game with terminal payoffs of players and polygonal constraints for players controls. Formalization of players' strategies in the game is based on formalization and the results of positional antagonistic differential games positional antagonistic differential games theory, developed by N. N. Krasovskii and his scientific school. The game is such, that it could be reduced to a game on the plane and the problem is transformed to solving non-standard optimal control problems. For the approximation of trajectories in these problems a set of computational geometry algorithms in plane is used, including convex hull construction, union and intersection of polygons and a Minkowski sum for polygons.
Keywords: nonantagonistic differential game, Nash solution, Stackelberg solution, algorithm. 
@article{CGTM_2009_2_a16,
     author = {Anatolii F. Kleimenov and Sergei I. Osipov and Dmitry R. Kuvshinov},
     title = {Nash and {Stackelberg} {Solutions} {Numerical} {Construction} in a {Two-Person} {Nonantagonistic} {Linear} {Positional} {Differential} {Game}},
     journal = {Contributions to game theory and management},
     pages = {205--219},
     publisher = {mathdoc},
     volume = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2009_2_a16/}
}
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Anatolii F. Kleimenov; Sergei I. Osipov; Dmitry R. Kuvshinov. Nash and Stackelberg Solutions Numerical Construction in a Two-Person Nonantagonistic Linear Positional Differential Game. Contributions to game theory and management, Tome 2 (2009), pp. 205-219. http://geodesic.mathdoc.fr/item/CGTM_2009_2_a16/