Geodesic
About optimum on risks and regrets situations in game of two persons
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 60-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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Non-cooperative game of two persons is considered. Quality of functioning of players is estimated by four-component vector criterion. Here an outcome (payoff), risk and regrets of players are considered. Concepts of optimum situations of non-cooperative game from the point of view of the stated vector estimates are considered. The example is given. Solution of game is based on the principle of guaranteed result and function of regret used by Savage. Existence of this solution is established.
Keywords: strategy; Nash equilibrium; maximin; Savage regret; Wald risk. 
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N. G. Soldatova. About optimum on risks and regrets situations in game of two persons. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 60-64. http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a7/

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[2] Bardin A. E., Zhiteneva Yu. N., Spektral'nye i evolyutsionnye zadachi, 22 (2012), 2–5 (in Russ.)

[3] V. I. Zhukovskiy, M. E. Salukvadze, The Vector-Valued Maximin, Academic Press, N.Y. etc., 1994, 282 pp. | MR | Zbl