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Matematicheskoe modelirovanie, 2010, Volume 22, Number 12, Pages 144–160 (Mi mm3058)  
This article is cited in 4 scientific papers (total in 4 papers)

Probability and possibility models of matrix games of two subjects

S. S. Papilin, Yu. P. Pytyev

Lomonosov Moscow State University, Faculty of Physics, Chair of Computer Methods in Physics
Full-text PDF (246 kB) Citations (4)
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Abstract: Probability models and their possibility counterparts of one-matrix and bimatrix games of two subjects (A and B) were defined and analyzed. For one-matrix game possibility model a theorem was proven saying that maximin and minimax fuzzy strategies exist and that possibilities of A win and B loss related to these strategies are equal.
The concepts of fuzzy and randomized game strategies were defined and analyzed. A problem of statistic modelling of A and B fuzzy strategies was resolved.
For bimatrix game possibility models the existence of equilibrium points was examined. For the problem of win possibility maximization it was proven that equilibrium points exist. For the problem of loss possibility minimization it was shown that if equilibrium points exist there are some of them related to unfussy A and B strategies.
Keywords: probability theory, possibility theory, game theory, matrix game, bimatrix game, minimax strategy, maximin strategy, equilibrium point.
Received: 15.03.2010
English version:
Mathematical Models and Computer Simulations, 2011, Volume 3, Issue 4, Pages 528–540
DOI: https://doi.org/10.1134/S2070048211040077
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. S. Papilin, Yu. P. Pytyev, “Probability and possibility models of matrix games of two subjects”, Matem. Mod., 22:12 (2010), 144–160; Math. Models Comput. Simul., 3:4 (2011), 528–540
Citation in format AMSBIB
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\by S.~S.~Papilin, Yu.~P.~Pytyev
\paper Probability and possibility models of matrix games of two subjects
\jour Matem. Mod.
\yr 2010
\vol 22
\issue 12
\pages 144--160
\mathnet{http://mi.mathnet.ru/mm3058}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2810221}
\transl
\jour Math. Models Comput. Simul.
\yr 2011
\vol 3
\issue 4
\pages 528--540
\crossref{https://doi.org/10.1134/S2070048211040077}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928984672}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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    References:52
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