Geodesic
Solutions of a~cooperative differential group pursuit game
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 2, pp. 57-78.

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In the paper the non-zero sum group pursuit game with $m$ pursuers and one evader is considered. A new approach to finding a solution of this kind of games is proposed. The key point of the paper is to construct а cooperative solution of the game (the core) and compare it with an non-cooperative solutions such as Nash equilibria. We prove that there exists an nonempty time-consistent core in this game. Ill. 3, bibl. 14.
Keywords: group pursuit game, Nash equilibrium, differential cooperative game, time-consistency.
Mots-clés : core 
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Ya. B. Pankratova. Solutions of a~cooperative differential group pursuit game. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 2, pp. 57-78. http://geodesic.mathdoc.fr/item/DA_2010_17_2_a4/

[1] Bondareva O. N., “Nekotorye primeneniya metodov lineinogo programmirovaniya k teorii kooperativnykh igr”, Problemy kibernetiki, 10, 119–140 | MR

[2] Petrosyan L. A., “Ob odnom semeistve differentsialnykh igr na vyzhivanie v prostranstve $\mathbb R^n$”, Dokl. AN SSSR, 161:1 (1965), 52–54 | MR | Zbl

[3] Petrosyan L. A., Differentsialnye igry presledovaniya, Izd-vo Leningr. un-ta, L., 1977, 224 pp. | MR | Zbl

[4] Petrosyan L. A., “Ustoichivost reshenii v differentsialnykh igrakh so mnogimi uchastnikami”, Vestn. Leningr. un-ta. Ser. 1, 1977, no. 4, 46–52 | Zbl

[5] Petrosyan L. A., Danilov N. N., “Ustoichivye resheniya v neantagonisticheskikh differentsialnykh igrakh s netransferabelnymi vyigryshami”, Vestn. Leningr. un-ta. Ser. 1, 1979, no. 1, 52–59 | MR | Zbl

[6] Petrosyan L. A., Tomskii G. V., Geometriya prostogo presledovaniya, Nauka, Novosibirsk, 1983, 140 pp. | MR

[7] Petrosyan L. A., Shiryaev V. D., “Prostoe presledovanie odnim presledovatelem dvukh presleduemykh”, Nekotorye voprosy differentsialnykh i integralnykh uravnenii i ikh prilozheniya, 3, Yakutsk. gos. un-t, Yakutsk, 1978, 103–108 | MR

[8] Isaaks R., “Differential games: a mathematical theory with applications to warfare and pursuit”, Control and optimization, Wiley Press, New York, 1965, 384 pp. | MR

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

[10] Pankratova Ya., Tarashnina S., “How many people can be controlled in a group pursuit game”, Theory and decision, 56, Kluwer Academic Publ., Amsterdam, 2004, 165–181 | MR

[11] Tarashnina S., “Nash equilibria in a differential pursuit game with one pursuer and $m$ evaders”, Game theory and applications, v. III, Nova Science Publ., N.Y., 1998, 115–123 | MR

[12] Tarashnina S., “Time-consistent solution of a cooperative group pursuit game”, Int. Game Theory Rev., 4 (2002), 301–317 | DOI | MR | Zbl

[13] Scarf H. E., “The core of an $n$-person game”, Econometrica, 35 (1967), 50–69 | DOI | MR | Zbl

[14] Shapley L., “On balanced sets and cores”, Nav. Res. Logist., 14 (1967), 453–460 | DOI