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Notions of equilibrium for differential games on intersecting game sets. (English. Russian original) Zbl 1358.49033
Differ. Equ. 52, No. 11, 1469-1480 (2016); translation from Differ. Uravn. 52, No. 11, 1522-1532 (2016).
Summary: We suggest new notions of conflict equilibrium and demonstrate a technique of their use for finding a solution in arbitrary game problems on a game set common for all players and especially in problems with side interests of players in the static and dynamic settings.
MSC:
49N70 Differential games and control
91A23 Differential games (aspects of game theory)
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[1] Isaacs, R., Differential Games, New York, 1965. Translated under the title Differentsial’nye igry, Moscow: Mir, 1967. · Zbl 0125.38001
[2] McKinsey, J.C.C., Introduction to the Theory of Games, New York-Toronto-London: McGraw-Hill, 1952. Translated under the title Vvedenie v teoriyu igr, Moscow: Gosudarstv. Izdat. Fiz.-Mat. Lit., 1960. · Zbl 0049.09510
[3] Von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behavior, Princeton: Princeton Univ. Press, 1953. Translated under the title Teoriya igr i ekonomicheskoe povedenie, Moscow: Nauka, 1970. · Zbl 0053.09303
[4] Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1974. · Zbl 0298.90067
[5] Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation under Conditions of Indeterminacy), Moscow: Nauka, 1977. · Zbl 0461.93001
[6] Vaisbord, E.M. and Zhukovskii, V.I., Vvedenie v differentsial’nye igry neskol’kikh lits i ikh prilozheniya (Introduction to Differential n-Person Games and Their Applications), Moscow: Sovet. Radio, 1980. · Zbl 0448.90072
[7] Vorob’ev, N.N., Osnovy teorii igr. Beskoalitsionnye igry (Principles of Game Theory: Noncooperative Games), Moscow: Nauka, 1984. · Zbl 0537.90097
[8] Chikrii, A.A., Konfliktno-upravlyaemye protsessy (Conflict-Controlled Processes), Kiev, 1992.
[9] Smol’yakov, E.R., Differential games on partially overlapping sets, Differ. Uravn., 47, 1793-1802, (2011) · Zbl 1236.91028
[10] Smol’yakov, E.R., Upravlenie konfliktami s pobochnymi interesami uchastnikov (Conflict Control with Side Interests of Participants), Saarbrucken, 2013.
[11] Smol’yakov, E.R., Teoriya antagonizmov i differentsial’nye igry (Theory of Conflicts and Differential Games), Moscow: Editorial URSS, 2000.
[12] Smol’yakov, E.R., Teoriya konfliktnykh ravnovesii (Theory of Conflict Equilibria), Moscow, 2005. · Zbl 1132.91006
[13] Smol’yakov, E.R., Metody resheniya konfliktnykh zadach (Solution Methods for Conflict Problems), Moscow, 2010.
[14] Smol’yakov, E.R., Obobshchennoe optimal’noe upravlenie i dinamicheskie konfliktnye zadachi (Generalized Optimal Control and Dynamical Conflict Problems), Moscow, 2010.
[15] Smol’yakov, E.R., Ravnovesnye modeli pri nesovpadayushchikh interesakh uchastnikov (Equilibrium Models in Which the Participants Have Different Interests), Moscow: Nauka, 1986.
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