The Optimal Control in Differential Two Person Game with Vector Payoff Functions and Expert Estimations

  • Д.С. Лобарёв Pskov State University (Pskov, Russia) Email: lds1979@mail.ru
  • С.И. Межов Altai State University (Barnaul, Russia) Email: megoff@mail.ru
DOI_disc_logo https://doi.org/10.14258/izvasu(2019)1-15
Keywords: mathematical models in economics, optimal control, differential game, expert estimations, Bellman equation

Abstract

The paper presents a solution of the differential game of two persons with vector-valued payoff function and expert evaluation. If there are several criteria, players need to seek a reasonable compromise which consists in choosing a control that delivers the best values simultaneously to all the criteria. For example, in the economy, it is necessary to achieve the maximum possible profit and output and, at the same time, a certain level of quality and profitability of the produced products. However, the presence of several criteria in the management problem is an expression of uncertainty which reflects the unclear knowledge of the players' own goals. Identifying a single target function solves this problem. One of the approaches involves the use of expert estimations, which are quantitative information about the relative importance of the components of the payoff func t ion, rel at ive to which t he line ar convolut ion is performed. Compromise vectors from experts allow us to reduce the game problem to a standard non-cooperative differential game which is solved by Bellman's equation. This algorithm helps us find the explicit form of an optimal solution.

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Author Biographies

Д.С. Лобарёв, Pskov State University (Pskov, Russia)
старший преподаватель кафедры математики и методики обучения математике; директор Ресурсного центра подготовки кадров для промышленности и социальной сферы Псковской области  
С.И. Межов, Altai State University (Barnaul, Russia)
доктор экономических наук, доцент, директор международного института экономики, менеджмента и информационных систем  

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Published
2019-03-06
How to Cite
Лобарёв Д., Межов С. The Optimal Control in Differential Two Person Game with Vector Payoff Functions and Expert Estimations // Izvestiya of Altai State University, 2019, № 1(105). P. 90-94 DOI: 10.14258/izvasu(2019)1-15. URL: http://izvestiya.asu.ru/article/view/%282019%291-15.
Issue
No 1(105) (2019): Izvestiya of Altai State University
Section
Математика и механика

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