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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 5, Pages 46–55 (Mi ivm8703)  
This article is cited in 2 scientific papers (total in 2 papers)

One class of simultaneous pursuit games

N. Yu. Satimova, G. I. Ibragimovb

a National University of Uzbekistan, Tashkent, Republic of Uzbekistan
b Institute of Mathematics and Information Technologies, Tashkent, Republic of Uzbekistan
Full-text PDF (198 kB) Citations (2)
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Abstract: Let $A$ and $B$ be given convex closed bounded nonempty subsets in a Hilbert space $H$; let the first player choose points in the set $A$ and let the second one do those in the set $B$. We understand the payoff function as the mean value of the distance between these points. The goal of the first player is to minimize the mean value, while that of the second player is to maximize it. We study the structure of optimal mixed strategies and calculate the game value.
Keywords: simultaneous game, mixed strategy, payoff function, optimal mixed strategies, game value.
Received: 25.05.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 5, Pages 39–46
DOI: https://doi.org/10.3103/S1066369X12050052
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: N. Yu. Satimov, G. I. Ibragimov, “One class of simultaneous pursuit games”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 5, 46–55; Russian Math. (Iz. VUZ), 56:5 (2012), 39–46
Citation in format AMSBIB
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\by N.~Yu.~Satimov, G.~I.~Ibragimov
\paper One class of simultaneous pursuit games
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 5
\pages 46--55
\mathnet{http://mi.mathnet.ru/ivm8703}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3076889}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 5
\pages 39--46
\crossref{https://doi.org/10.3103/S1066369X12050052}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862675804}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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