Numerical construction algorithm for Nash solutions in a two-person positional differential game
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 81-90 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article presents a numerical algorithm for building an approximation of the Nash solution set in a linear non-zero sum positional differential two-person game with terminal cylindrical cost functionals and geometrical constraints on players' controls.
Keywords: positional differential games, Nash equilibrium solution, numerical algorithm.
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D. R. Kuvshinov. Numerical construction algorithm for Nash solutions in a two-person positional differential game. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 81-90. http://geodesic.mathdoc.fr/item/VUU_2009_3_a5/

[1] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[2] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 520 pp. | MR

[3] Kleimenov A. F., Neantagonisticheskie pozitsionnye differentsialnye igry, Nauka, Ekaterinburg, 1993, 184 pp. | MR

[4] Isakova E. A., Logunova G. V., Patsko V. S., “Postroenie stabilnykh mostov v lineinoi differentsialnoi igre s fiksirovannym momentom okonchaniya”, Algoritmy i programmy resheniya lineinykh differentsialnykh igr (materialy po matematicheskomu obespecheniyu EVM), IMM UNTs AN SSSR, Sverdlovsk, 1984, 127–158

[5] Tarasev A. M., Ushakov V. N., Khripunov A. P., “Ob odnom vychislitelnom algoritme resheniya igrovykh zadach upravleniya”, Prikladnaya matematika i mekhanika, 51:2 (1987), 216–222 | MR | Zbl

[6] Osipov S. I., “O realizatsii algoritma postroeniya reshenii dlya klassa ierarkhicheskikh igr Shtakelberga”, Avtomatika i telemekhanika, 2007, no. 11, 195–208 | MR

[7] Osipov S. I., Reshenie odnogo klassa ierarkhicheskikh differentsialnykh igr (metody, algoritmy, programmy), dis. No 8230; kand. fiz.-matem. nauk, UrGU, Ekaterinburg, 2007, 128 pp.

[8] Kuvshinov D. R., “Algoritm chislennogo postroeniya reshenii po Neshu v pozitsionnoi differentsialnoi igre dvukh lits”, Dinamicheskie sistemy, upravlenie i nanomekhanika, Tez. dokl. Vseross. konf., Izhevsk, 2009, 42