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, 2024, Issue 3,Pages <nobr>18

Poincaré method of small parameter for construction of equilibria

V. I. Zhukovskii^a, L. V. Zhukovskaya^b, S. N. Sachkov^c, E. N. Sachkova^c

^a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Leninskie Gory, Moscow, 119991, Russia
^b Central Economic and Mathematical Institute of the Russian Academy of Sciences, Nakhimovskii pr., 47, Moscow, 117418,Russia
^c State University of Humanities and Technology, ul. Zelenaya, 22, Orekhovo-Zuevo, 142611, Russia

Abstract: 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

UDC: 519.62

MSC: 91A10

Language: English