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Taurida Journal of Computer Science Theory and Mathematics, 2021 Issue 1, Pages 7–31 (Mi tvim107)

Uncertainty and discrete maximin

V. I. Zhukovskiia, L. V. Smirnovab

a Moscow State University named after Lomonosov, Faculty of Computational Mathematics and Cybernetics, Department of Optimal Control, Leninskiye Gory, GSP-1, Moscow, 119991, Russia
b State University of Humanities and Technology, Zelenaya, 22, Orekhovo-Zuevo, 142611, Russia

Abstract: The article consists of two parts. The first part is devoted to general questions that are related to uncertainty: causes and sources of uncertainties appearance, classification of uncertainties in economic systems and approach to their assessment. In the second part the concept of maximin, based on the principle of guaranteed result (Wald's principle) is considered. In this case, maximin is interpreted from viewpoint of two-level hierarchical game. On the basis of the maximin concept, a guaranteed solution in outcomes for K-stage positional single-criterion linearquadratic problem under uncertainty is formalized. An explicit form of the guaranteed solution for this problem is found.

Keywords: Nash equilibrium, Berge equilibrium, uncertainty, maximin, difference (multi-stage) system.

UDC: 519.833.2

MSC: 91A10

Language: English

DOI: 10.37279/1729-3901-2021-20-1-7-31



© Steklov Math. Inst. of RAS, 2024