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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.
49N70 Differential games and control
91A23 Differential games (aspects of game theory)
Full Text: DOI
[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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