Differential game theory application in models of trade relations of Great Britain with Portugal and Russia with Belarus

Abstract

The article includes the analysis of the current state of differential games theory based on the maximum principle of academician L. S. Pontryagin. The optimal solution of conflict, but not (strictly) analytical games and the question of the uniqueness of the optimal solution are investigated. The author composes and analyzes a system of four nonlinear ordinary differential equations with parameters, and their (dynamic) variation leads to the improvement of successive approximations of the exact solution, the finding of which is very problematic. The article includes several examples: the model of military operations with a certain arsenal and the analysis of two non-antagonistic games - the dynamic model of trade between Great Britain and Portugal, as well as between Russia and Belarus.The article shows how the problem of differential economic-mathematical game arises from the simplest problems of classical variational calculus. Sufficient conditions for the PontryaginMangasarian maximum and their applications to the study of economic problems are investigated. The transition to the study of the continuously differential game of international trade is shown. Possible strategies of players’ behavior in non-antagonistic (positional) games are investigated. The problem of the lack of statistical information (base) is reduced to the study of not absolute, but relative values of phase variables, which is guaranteed by the stable structure of the corresponding economic and statistical model. The conclusions can be useful for undergraduate and postgraduate students of economic and mathematical profile. The implementation of the proposed development of the author assumes the existence of a strong base of economic-statistical (experimental) data and the emphasis of the relevant decision-maker. The results of the article can be useful for the practice of analysis and forecasting.

Keywords

• differential games
• antagonistic games
• non zero-sum games
• coalitional games
• dynamic games
• trade relations