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Russia Moscow; OrekhovoZuevo
Section  Mathematics 
Title  Method of settlement of conflicts under uncertainty 
Author(s)  Zhukovskii V.I.^{a}, Soldatova N.G.^{b} 
Affiliations  Lomonosov Moscow State University^{a}, Moscow State Regional Institute of Humanities^{b} 
Abstract  As a mathematical model of conflict the noncooperation 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 twolevel 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, noncooperative game, Nash equilibrium, Slater maximum and minimum 
UDC  519.833 
MSC  91A10 
DOI  10.20537/vm130303 
Received  5 July 2013 
Language  Russian 
Citation  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. 2833. 
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