Multistep Bertrand duopoly model with imports

V. I. Zhukovskii, M. V. Boldyrev

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Department of Optimal Control, Leninskiye Gory ul., 1, bldg. 52, Moscow, 119234, Russian Federation

Abstract: Through the use of a suitable variant of dynamic programming, the explicit form of the situation of guaranteed equilibrium in a two-step positional mathematical model of Bertrand duopoly has been found. This research may be extended by examination of $ N $-person games as well as applying the Berge equilibrium instead of the Nash equilibrium.

Keywords: dynamic programming, strongly guaranteed equilibrium, Bertrand duopoly, uncertainty, Nash equilibrium, game theory.

UDC: 519.532.2

MSC: 90С39

Language: English