Geodesic
Reductions of interval noncooperative games
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2001-2008
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Noncooperative games of a finite number of persons with interval-valued payoff functions are considered. The concept of an equilibrium situation is introduced. A reduction of such games to deterministic noncooperative games is proposed. Properties of the reduced games are discussed. Interval antagonistic and bimatrix games are examined, and illustrative examples are considered. 
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L. T. Ashchepkov; D. V. Davydov. Reductions of interval noncooperative games. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2001-2008. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a6/

[1] Neiman Dzh., Morgenshtern O., Teoriya igr i ekonomicheskoe povedenie, Nauka, M., 1970 | MR

[2] Vorobev H. H., Osnovy teorii igr. Beskoalitsionnye igry, Nauka, M., 1984 | MR

[3] Nash J., “Non-cooperative games”, Ann. Math., 54:2 (1951), 286–295 ; H. H. Vorobev (red.), Matrichnye igry, Fizmatgiz, M., 1961, 205–221 | DOI | MR | Zbl

[4] Mak-Kinsi Dzh., Vvedenie v teoriyu igr, Fizmatgiz, M., 1960

[5] Ouen G., Teoriya igr, Mir, M., 1971 | MR | Zbl

[6] Petrosyan L. A., Zenkevich H. A., Semina E. A., Teoriya igr, Vyssh. shkola, Knizhnyi dom “Universitet”, M., 1998 | MR | Zbl

[7] Gusev Yu. M., Efanov V. N., Krymskii V. G., Rutkovskii V. Yu., “Analiz i sintez lineinykh intervalnykh dinamicheskikh sistem (sostoyanie problemy). I, II”, Izv. AN SSSR. Tekhn. kibernetika, 1991, no. 1, 3–23 ; No 2, 3–30 | MR | Zbl

[8] Aschepkov L. T., Davydov D. V., “Stabilizatsiya nablyudaemoi lineinoi sistemy upravleniya s postoyannymi intervalnymi koeffitsientami”, Izv. vuzov. Matematika, 2002, no. 2(477), 11–17

[9] Aschepkov L. T., Kolpakova G. E., Stegostenko Yu. B., “Stabilizatsiya nestatsionarnoi lineinoi diskretnoi sistemy upravleniya s intervalnymi koeffitsientami po nablyudeniyam fazovykh sostoyanii”, Avtomatika i telemekhan., 2002, no. 5, 3–11

[10] Davydov D. V., “Lokalnaya stabilizatsiya intervalno nablyudaemoi sistemy s neopredelennymi parametrami”, Vychisl. tekhnologii, 8:1 (2003), 44–51 | Zbl

[11] Aschepkov L. T., Kosogorova I. B., “Minimizatsiya kvadratichnoi funktsii s intervalnymi koeffitsientami”, Zh. vychisl. matem. i matem. fiz., 42:5 (2002), 653–664 | MR

[12] Aschepkov L. T., Milyutin A. B., “Upravlenie zapasami s ogranichennym srokom khraneniya v usloviyakh intervalnosti sprosa”, Tr. XIII Baikalskoi mezhdunar. shkoly-seminara “Metody optimizatsii i ikh prilozheniya” (2–8 iyulya 2005 g., Irkutsk-Severobaikalsk), v. 4, Intervalnyi analiz, ISEM SO RAN, Irkutsk, 2005, 27–33

[13] Dombrovskii V. V., Chausova E. V., “Dinamicheskaya setevaya model upravleniya zapasami s intervalnoi neopredelennostyu sprosa”, Tr. Mezhdunar. konf. RDAMM-2001, Ch. 2. Spets. vyp. S, v. 6, 2001, 271–274

[14] Levin V. I., “Sravnenie intervalnykh velichin i optimizatsiya neopredelennykh sistem”, Informatsionnye tekhnologii, 1998, no. 7, 22–32

[15] Aschepkov L. T., Gutorova S. V., Karpachev A. A., Li S., “Intervalnye matrichnye igry”, Dalnevostochnyi matem. zhurnal, 2003, no. 2, 276–288

[16] Shashikhin V. N., “Reshenie intervalnoi matrichnoi igry v smeshannykh strategiyakh”, Izv. RAN. Teoriya i sistemy upravleniya, 2001, no. 5, 97–104 | MR | Zbl

[17] Rohn J., Kreslova J., “Linear interval inequalities”, Linear and Multilinear Algebra, 38 (1994), 41–43. | MR