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Section
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Mathematics
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Title
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Method of settlement of conflicts under uncertainty
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Author(-s)
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Zhukovskii V.I.a,
Soldatova N.G.b
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Affiliations
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Lomonosov Moscow State Universitya,
Moscow State Regional Institute of Humanities (State University of Humanities and Technology)b
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Abstract
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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.
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Keywords
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strategy, situations, uncertainty, non-cooperative game, Nash equilibrium, Slater maximum and minimum
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UDC
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519.833
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MSC
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91A10
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DOI
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10.20537/vm130303
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Received
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5 July 2013
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Language
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Russian
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Citation
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Zhukovskii V.I., Soldatova N.G. Method of settlement of conflicts under uncertainty, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 3, pp. 28-33.
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References
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- Zhukovskii V.I., Kudryavtsev K.N. Equilibrating conflicts under uncertainty. I. Analogue of a saddle-point, Mat. Teor. Igr Pril., 2013, vol. 5, no. 1, pp. 27-44.
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Full text
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