Geodesic
Probability and possibility models of matrix games of two subjects
Matematičeskoe modelirovanie, Tome 22 (2010) no. 12, pp. 144-160.

Voir la notice de l'article provenant de la source Math-Net.Ru

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, minimax strategy, maximin strategy, equilibrium point.
Mots-clés : matrix game, bimatrix game 
@article{MM_2010_22_12_a10,
     author = {S. S. Papilin and Yu. P. Pytyev},
     title = {Probability and possibility models of matrix games of two subjects},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {144--160},
     publisher = {mathdoc},
     volume = {22},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_12_a10/}
}
TY  - JOUR
AU  - S. S. Papilin
AU  - Yu. P. Pytyev
TI  - Probability and possibility models of matrix games of two subjects
JO  - Matematičeskoe modelirovanie
PY  - 2010
SP  - 144
EP  - 160
VL  - 22
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2010_22_12_a10/
LA  - ru
ID  - MM_2010_22_12_a10
ER  - 
%0 Journal Article
%A S. S. Papilin
%A Yu. P. Pytyev
%T Probability and possibility models of matrix games of two subjects
%J Matematičeskoe modelirovanie
%D 2010
%P 144-160
%V 22
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2010_22_12_a10/
%G ru
%F MM_2010_22_12_a10
S. S. Papilin; Yu. P. Pytyev. Probability and possibility models of matrix games of two subjects. Matematičeskoe modelirovanie, Tome 22 (2010) no. 12, pp. 144-160. http://geodesic.mathdoc.fr/item/MM_2010_22_12_a10/

[1] Lyus R. D., Raifa Kh., Igry i resheniya. Vvedenie i kriticheskii obzor, Izdatelstvo inostrannoi literatury, M., 1961, 642 pp. | MR

[2] Ouen G., Teoriya igr, Mir, M., 1971, 230 pp. | MR | Zbl

[3] Pytev Yu. P., Vozmozhnost kak alternativa veroyatnosti, Fizmatlit, M., 2007, 464 pp.

[4] Germeier Yu. B., Igry s neprotivopolozhnymi interesami, Nauka, M., 1976, 328 pp. | MR | Zbl

[5] Orlovskii S. A., Problemy prinyatiya reshenii pri nechetkoi iskhodnoi informatsii, Nauka, M., 1981, 194 pp. | MR