Geodesic
Application of Lyapunov–Poincar\'{e} method of small parameter for Nash and Berge equilibrium designing in one differential two-player game
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 4, pp. 601-624

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The Poincaré small parameter method is actively used in celestial mechanics, as well as in the theory of differential equations and in its important section called optimal control. In this paper, the mentioned method is used to construct an explicit form of Nash and Berge equilibrium in a differential positional game with a small influence of one of the players on the rate of change of the state vector.
Keywords: small parameter method, differential linear-quadratic noncooperative game, Nash equilibrium, Berge equilibrium 
@article{VUU_2023_33_4_a4,
     author = {V. I. Zhukovskii and L. V. Zhukovskaya and S. N. Sachkov and E. N. Sachkova},
     title = {Application of {Lyapunov{\textendash}Poincar\'{e}} method of small parameter for {Nash} and {Berge} equilibrium designing in one differential two-player game},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     publisher = {mathdoc},
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     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a4/}
}
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V. I. Zhukovskii; L. V. Zhukovskaya; S. N. Sachkov; E. N. Sachkova. Application of Lyapunov–Poincar\'{e} method of small parameter for Nash and Berge equilibrium designing in one differential two-player game. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 4, pp. 601-624. http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a4/