Pareto equilibrium of objections and counterobjections in a differential game of three persons
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 1, pp. 39-72.

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The linear-quadratic positional differential game of three persons is considered. The coefficient criteria are established, here when they are realized there is no Nash equilibrium situation in the game and at the same time there is an equilibrium of objections and counterobjections.
Keywords: noncooperative games; Nash equilibrium; active equilibrium; equilibrium of objections and counterobjections.
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Vladislav I. Zhukovskii; Juliya N. Zhiteneva; Juliya A. Belskikh. Pareto equilibrium of objections and counterobjections in a differential game of three persons. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 1, pp. 39-72. http://geodesic.mathdoc.fr/item/MGTA_2019_11_1_a2/

[1] Bolshoi tolkovyi slovar russkogo yazyka, Norint, Sankt-Peterburg, 2003

[2] Vaisbord E. M., “O koalitsionnykh differentsialnykh igrakh”, Differentsialnye uravneniya, 10:4 (1974), 613–623 | Zbl

[3] Vaisbord E. M., Zhukovskii V. I., Vvedenie v differentsialnye igry neskolkikh lits i ikh prilozheniya, Sovetskoe radio, M., 1980

[4] Vilkas E. I., “Formalizatsiya problemy vybora teoretiko-igrovogo kriteriya optimalnosti”, Sb. statei, Matematicheskie metody v sotsialnykh naukakh, 2, In-t matematiki i kibernetiki AN Lit. SSR, Vilnyus, 1972, 9–55 | MR

[5] Vilkas E. I., Maiminas E. Z., Resheniya: teoriya, informatsiya, modelirovanie, Radio i svyaz, M., 1981

[6] Voevodin V. V., Kuznetsov Yu. A., Matritsy i vychisleniya, Nauka, M., 1984

[7] Gantmakher F. R., Teoriya matrits, Fizmatlit, M., 2004

[8] Zhukovskii V. I., Vvedenie v differentsialnye igry pri neopredelennosti. Ravnovesie ugroz i kontrugroz, KRASAND, M., 2010

[9] Zhukovskii V. I., Gorbatov A. S., Kudryavtsev K. N., “Ravnovesie po Neshu i po Berzhu v odnoi lineino-kvadratichnoi igre”, Matematicheskaya teoriya igr i ee prilozheniya, 9:1 (2017), 62–94 | Zbl

[10] Zhukovskii V. I., Kudryavtsev K. N., Samsonov S. V., Vysokos M. I., Belskikh Yu. A., “Klass differentsialnykh igr, v kotorykh otsutstvuet ravnovesie po Neshu, no suschestvuet ravnovesie ugroz i kontrugroz”, Vestnik Yuzhno-Uralskogo universiteta. Seriya Matematika, Mekhanika, Fizika, 10:2 (2018), 5–21

[11] Zhukovskii V. I., Tynyanskii N. T., Ravnovesnye upravleniya mnogokriterialnykh dinamicheskikh zadach, KRASAND, M., 2010

[12] Zhukovskii V. I., Chikrii A. A., Differentsialnye uravneniya. Lineino-kvadratichnye differentsialnye igry, Uchebnoe posobie dlya VUZov, Yurait, M., 2017

[13] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1984

[14] Lyus R. D., Raifa Kh., Igry i resheniya, Inostrannaya literatura, M., 1961

[15] Mamedov M. B., “O ravnovesii po Neshu situatsii, optimalnoi po Pareto”, Izv. AN Azerbaidzhana. Seriya fiz.-tekh. nauk, 4:2 (1983), 11–17

[16] Ouen G., Teoriya igr, Mir, M., 1971

[17] Podinovskii V. V., Nogin V. D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, Fizmatlit, M., 2007

[18] Smolyakov E. R., Teoriya konfliktnykh ravnovesii, URSS, M., 2005

[19] Biltchev S. V., “$\varepsilon-Z$-Equilibrium in a Differential Game Described by a Parabolic System”, Many Players Differential Game, Technical Univ., Bulgaria, Rousse, 1984, 47–52

[20] Case J. H., “A class of games having Pareto optimal Nash equilibrium”, J. Optimiz. Theory Appl., 13:3 (1974), 378–385 | DOI | MR

[21] Dochev D. T., Stojanov N. V., “Existence of $Z$-Equilibrium in a Differential Game with Delay”, Many Players Differential Game, Technical Univ., Bulgaria, Rousse, 1984

[22] Gaidov S. D., “$Z$-Equilibrium in Stochastic Differential Game”, Many Players Differential Game, Technical Univ., Bulgaria, Rousse, 1984 | MR

[23] Nash J., “Equillibrium points in N-person games”, Proc. Nat. Academ. Sci. USA, 36 (1950), 48–49 | DOI | MR | Zbl

[24] Nash J., “Non-cooperative games”, Annales of Mathematics, 54 (1951), 286–295 | DOI | MR | Zbl

[25] Rashkov P. I., “Sufficient Conditions for $Z$-Equilibrium in a Differential Game in Banach Spase”, Many Players Differential Game, Technical Univ., Bulgaria, Rousse, 1984, 91–99

[26] Tersian St. A., “On the $Z$-Equilibrium Points in a Differential Game”, Many Players Differential Game, Technical Univ., Bulgaria, Rousse, 1984, 106–111

[27] Zhukovskii V. I., “Some Problems of Non-Antagonistic Differential Games”, Mathematical Method in Operation Research, Academy of Sciences, Bulgaria, Sofia, 1985, 103–195

[28] Zhukovskii V. I., Kudryavtsev K. N., “Coalition equilibrium in a three-person game”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA, dedicated to the memory of V. F. Demyanov (St. Petersburg, 22–27 May 2017), 1–4

[29] Zhukovskii V. I., Salukvadze M. E., The Vector-Valued Maximin, Academic Press, N.Y. etc., 1994 | MR