Geodesic
The Pareto-optimality of Nash equilibrium in dynamic controlled systems with conflict
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 984-996 
M. B. Mamedov. The Pareto-optimality of Nash equilibrium in dynamic controlled systems with conflict. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 984-996. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a1/
@article{ZVMMF_1990_30_7_a1,
     author = {M. B. Mamedov},
     title = {The {Pareto-optimality} of {Nash} equilibrium in dynamic controlled systems with conflict},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {984--996},
     year = {1990},
     volume = {30},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a1/}
}
TY  - JOUR
AU  - M. B. Mamedov
TI  - The Pareto-optimality of Nash equilibrium in dynamic controlled systems with conflict
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 984
EP  - 996
VL  - 30
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a1/
LA  - ru
ID  - ZVMMF_1990_30_7_a1
ER  - 
%0 Journal Article
%A M. B. Mamedov
%T The Pareto-optimality of Nash equilibrium in dynamic controlled systems with conflict
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 984-996
%V 30
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a1/
%G ru
%F ZVMMF_1990_30_7_a1

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

Sufficient conditions are derived for the Pareto-optimality of an equilibrium. A class of positional differential games satisfying these conditions are considered. In other words, equilibria that are unimprovable in the equilibrium set are Pareto-optimal, i.e., unimprovable among all the situations of the game.

[1] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR | Zbl

[2] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985 | MR

[3] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981 | MR

[4] Kononenko A. F., “O ravnovesnykh pozitsionnykh strategiyakh v neantagonisticheskikh differentsialnykh igrakh”, Dokl. AN SSSR, 231:2 (1976), 286–288 | MR

[5] Kononenko A. F., “Struktura optimalnoi strategii v dinamicheskikh upravlyaemykh sistemakh”, Zh. vychisl. matem. i matem. fiz., 20:5 (1980), 1105–1116 | MR | Zbl

[6] Tynyanskii N. T., Zhukovskii V. I., “Differentsialnye igry s nenulevoi summoi”, Itogi nauki i tekhn. Matem. analiz, 17, VINITI, M., 1979

[7] Mamedov M. B., “O ravnovesnosti po Neshu situatsii, optimalnoi po Pareto v differentsialnykh igrakh dvukh lits”, Izv. AN AzerbSSR. Fiz.-tekhn. i matem. nauki, 1983, no. 2, 111–117 | MR | Zbl

[8] Mamedov M. B., O dostatochnykh usloviyakh Pareto optimalnosti situatsii ravnovesiya v differentsialnykh igrakh, Dep. v VINITI, No 4742-86

[9] Mamedov M. B., Vychislenie tseny nekotorykh pozitsionnykh differentsialnykh igr i o suschestvovanii Pareto-optimalnoi situatsii ravnovesiya, Dep. v VINITI, No 4011-V88

[10] Konurbaev E. M., “Metody poiska effektivnykh ravnovesnykh situatsii v differentsialnykh igrakh mnogikh lits”, Zh. vychisl. matem. i matem. fiz., 25:8 (1985), 1260–1262 | MR

[11] Prokopev V. A., “O suschestvovanii ustoichivykh reshenii v odnom klasse kooperativnykh differentsialnykh igr”, Neantagonistich. differents. igry i ikh prilozh., VZMI, M., 1986, 98–101

[12] Li E. B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972 | MR

[13] Blagodatskikh V. I., “Nekotorye rezultaty po teorii differentsialnykh vklyuchenii”, obzor, Difford 1974, Summer School on Ordinary Different. Equat., 29–66

[14] Subbotin A. I., “Vychislenie tseny differentsialnoi igry sblizheniya prostykh dvizhenii na ogranichennom promezhutke vremeni”, Upravlenie s garantirovannym rezultatom, UNTs AN SSSR, Sverdlovsk, 1987, 71–76

[15] Chistyakov Yu. E., Struktura i svoistva resheniya pozitsionnoi differentsialnoi igry mnogikh lits, Dis. ...kand. fiz.-matem. nauk, VTs AN SSSR, M., 1986

[16] Podinovskii V. V., Nogin V. D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, Nauka, M., 1982 | MR