Geodesic
Poincaré method of small parameter for construction of equilibria
Taurida Journal of Computer Science Theory and Mathematics, no. 3 (2024), pp. 18-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a differential linear-quadratic noncooperative positional game, in which one of the players has a small influence on the rate of change of the state vector. For this game, the coefficient criteria for the existence of Berge and Nash equilibria are established and a design procedure for such equilibria is suggested, on the basis of dynamic programming combined with the small parameter method.
Keywords: small parameter method, differential linear-quadratic noncooperative game, Nash equilibrium, Berge equilibrium 
@article{TVIM_2024_3_a1,
     author = {V. I. Zhukovskii and L. V. Zhukovskaya and S. N. Sachkov and E. N. Sachkova},
     title = {Poincar\'e method of small parameter for construction of equilibria},
     journal = {Taurida Journal of Computer Science Theory and Mathematics},
     pages = {18--43},
     year = {2024},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVIM_2024_3_a1/}
}
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V. I. Zhukovskii; L. V. Zhukovskaya; S. N. Sachkov; E. N. Sachkova. Poincaré method of small parameter for construction of equilibria. Taurida Journal of Computer Science Theory and Mathematics, no. 3 (2024), pp. 18-43. http://geodesic.mathdoc.fr/item/TVIM_2024_3_a1/