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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki: Year: Volume: Issue: Page: Find

 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 3, Pages 28–33 (Mi vuu387)

MATHEMATICS

Method of settlement of conflicts under uncertainty

V. I. Zhukovskiia, N. G. Soldatovab

a Department of Optimal Control, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russia
b Department of Mathematics and Physics, Moscow State Regional Institute of Humanities, Zelenaya, 22, Orekhovo-Zuevo, 142611, Russia

Abstract: As a mathematical model of conflict the non-cooperation game $\Gamma$ of two players under uncertainty is considered. About uncertainty only the limits of change are known. Any characteristics of probability are absent. To estimate risk in $\Gamma$ we use Savage functions of risk (from principle of minimax regret). The quality of functioning of conflict's participants is estimated according to two criteria: outcomes and risks, at that each of the participants tries to increase the outcome and simultaneously to decrease the risk. On the basis of synthesis of principles of minimax regret and guaranteed result, Nash equilibrium and Slater optimality as well as solution of the two-level hierarchical Stackelberg game, the notion of guaranteed equilibrium in $\Gamma$ (outcomes (prize) and risks) is formalized. We give the example. Then the existence of such a solution in mixed strategies at usual limits in mathematical game theory is established.

Keywords: strategy, situations, uncertainty, non-cooperative game, Nash equilibrium, Slater maximum and minimum.

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Document Type: Article
UDC: 519.833
MSC: 91A10

Citation: V. I. Zhukovskii, N. G. Soldatova, “Method of settlement of conflicts under uncertainty”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 3, 28–33

Citation in format AMSBIB
\Bibitem{ZhuSol13} \by V.~I.~Zhukovskii, N.~G.~Soldatova \paper Method of settlement of conflicts under uncertainty \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2013 \issue 3 \pages 28--33 \mathnet{http://mi.mathnet.ru/vuu387}