Geodesic
Regularization methods with penalty functions for finding nash equilibria in a bilinear nonzero-sum two-person game
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 5, pp. 813-823 
A. S. Antipin; F. P. Vasil'ev; A. Delavarkhalafi. Regularization methods with penalty functions for finding nash equilibria in a bilinear nonzero-sum two-person game. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 5, pp. 813-823. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_5_a4/
@article{ZVMMF_2005_45_5_a4,
     author = {A. S. Antipin and F. P. Vasil'ev and A. Delavarkhalafi},
     title = {Regularization methods with penalty functions for finding nash equilibria in a bilinear nonzero-sum two-person game},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {813--823},
     year = {2005},
     volume = {45},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_5_a4/}
}
TY  - JOUR
AU  - A. S. Antipin
AU  - F. P. Vasil'ev
AU  - A. Delavarkhalafi
TI  - Regularization methods with penalty functions for finding nash equilibria in a bilinear nonzero-sum two-person game
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 813
EP  - 823
VL  - 45
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_5_a4/
LA  - ru
ID  - ZVMMF_2005_45_5_a4
ER  - 
%0 Journal Article
%A A. S. Antipin
%A F. P. Vasil'ev
%A A. Delavarkhalafi
%T Regularization methods with penalty functions for finding nash equilibria in a bilinear nonzero-sum two-person game
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 813-823
%V 45
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_5_a4/
%G ru
%F ZVMMF_2005_45_5_a4

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

Bilinear nonzero-sum two-person games are considered. For solving this class of games, it is proposed to combine regularization methods (namely, the stabilization, residual, and quasi-solution methods) with penalty functions. The convergence of the methods is examined, and a regularizing operator is constructed.

[1] Nash J. F. Jr., “Equilibrium points in $n$-person games”, Proc. Nat. Acad. Sci. USA, 36 (1950), 48–49 | DOI | MR | Zbl

[2] Aubin J.-P., Frankowska H., Set valued analysis, Birkhauser, Boston etc., 1990 | MR | Zbl

[3] Antipin A. S., Delavarkhalafi A., “Metody resheniya bilineinykh igr dvukh lits s nenulevoi summoi”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 2002, no. 1, 40–47

[4] Vasilev F. P., Ivanitskii A. Yu., Lineinoe programmirovanie, Faktorial, M., 1998 | MR

[5] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1986 | MR | Zbl

[6] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Nauka, M., 1995 | MR

[7] Vasilev F. P., Metody optimizatsii, Faktorial, M., 2001 | Zbl

[8] Vasilev F. P., Antipin A. S., “Metody stabilizatsii dlya resheniya zadach ravnovesnogo programmirovaniya s netochno zadannym mnozhestvom”, Zh. vychisl. matem. i matem. fiz., 39:11 (1999), 1779–1786 | MR

[9] Antipin A. S., Vasilev F. P., “Metody nevyazki dlya resheniya ravnovesnykh zadach s netochno zadannym mnozhestvom”, Zh. vychisl. matem. i matem. fiz., 41:1 (2001), 3–8 | MR | Zbl

[10] Antipin A. S., Vasilev F. P., “Metod kvazireshenii dlya resheniya zadachi ravnovesnogo programmirovaniya s netochno zadannym mnozhestvom”, Vestn. Ros. un-ta Druzhby narodov. Ser. matem., 8:2 (2002), 3–11 | MR

[11] Antipin A. S., Vasilev F. P., “Metody regulyarizatsii dlya resheniya zadachi ravnovesnogo programmirovaniya s netochnymi vkhodnymi dannymi, osnovannye na rasshirenii mnozhestva”, Zh. vychisl. matem. i matem. fiz., 42:8 (2002), 1158–1165 | MR | Zbl

[12] Antipin A. S., “Rasscheplenie gradientnogo podkhoda dlya resheniya ekstremalnykh vklyuchenii”, Zh. vychisl. matem. i matem. fiz., 38:7 (1998), 1118–1132 | MR | Zbl