Literature cited
T. G. Abramyants, E. P. Maslov, and E. Ya. Rubinovich, “Three person differential games under conditions of indeterminacy,” in: Thesis Reports of the Fourth All-Union Conference “Statistical Methods in Control Theory” [in Russian], Frunze (1978), pp. 58–62.
V. V. Al'sevich, “Minimization of nonsmooth functions on the set of finite states of a dynamical system,” Differents. Uravn.,10, No. 2, 349–350 (1974).
V. V. Al'sevich, “The problem of terminal control with nondifferentiable quality criteria,” in: Differential and Integral Equations [in Russian], Vol. 2, Irkutsk (1973), pp. 81–87.
V. V. Al'sevich, “Necessary conditions for optimality for minimax problems of optimization,” Differents. Uravn.,12, No. 8, 1384–1391 (1976).
É. M. Balychavtsev and É. K. Lavrovskii, “On the structure of Pareto sets in some optimization problems,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 44–53 (1977).
R. E. Bellman, I. Glicksberg, and O. Gross, Some Questions of the Mathematical Theory of Control Processes [Russian translation], IL, Moscow (1962).
L. M. Boichuk and V. O. Ovchinnikov, “Basic approaches to solving multicriterial optimization problems (survey),” Avtomatika, No. 3, 3–7 (1973).
O. N. Bondareva, V. B. Vilkov, T. E. Kulakovskaya, N. M. Naumova, and N. A. Sokolina, “Survey of Soviet papers on the theory of cooperative games,” in: Operations Research and Statistical Modeling [in Russian], Vol. 4, Leningrad. Univ. (1977), pp. 81–126.
V. I. Borisov, “Problems of vector optimization,” in: Operations Research [in Russian], Nauka, Moscow (1972), pp. 72–91.
L. F. Burlyaeva, V. V. Kafarov, R. E. Kuzin, and A. V. Netushil, “Methods of search for Paretooptimal solutions in control problems of chemicotechnological processes,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 4, 196–199 (1976).
É. M. Vaisbord, V. I. Zhukovskii, and V. S. Molostvov, “Some results on optimal strategies in N person differential games,” in: Abstracts of the Third All-Union Conference on Game Theory [in Russian], Odessa (1974), pp. 30–31.
S. Vankrinene, “Nonantagonistic dynamical two-person games,” Author's Abstract of Candidates Dissertation, Vilnius (1972).
S. Vankrinene, “Cooperative dynamical two-person games,” Litov. Mat. Sb.,10, No. 3, 453–461 (1970).
Z. Varga, Antagonistic Differential Games with Vector Payoff Functions [in Russian], Moscow State University (1977).
Z. Varga, “On a cooperative pursuit game,” Vestn. Mosk. Gos. Univ., Ser. Vychisi. Mat. Kibern., No. 1 (1979).
V. V. Velichenko, “On sufficient conditions for a global minimax,” Dokl. Akad. Nauk SSSR,219, No. 5, 1045–1048 (1974).
V. V. Velichenko, “On the method of a field of extremals in sufficient conditions for optimality,” Zh. Vychisl. Mat. Mat. Fiz.,14, No. 1, 45–67 (1974).
V. V. Velichenko, “On conditions for a minimax in a multicriterial problem of optimal control,” in: Numerical Methods of Nonlinear Programming [in Russian], Materials of the First All-Union Seminar, Kiev (1976), pp. 19–26.
É. I. Vilkas, “Formalization of problems of choice of game-theoretic optimality criteria,” in: Mathematical Methods in the Social Sciences [in Russian], Vol. 2, Vilnius (1973), pp. 9–31.
É. I. Vilkas, “On cooperative solutions of games in the form of characteristic functions,” in: Mathematical Methods in the Social Sciences [in Russian], Vol. 2, Vilnius (1973), pp. 51–73.
É. Vilkas, “Multigoal optimization,” in: Mathematical Methods in the Social Sciences [in Russian], Vol. 7, Vilnius (1976), pp. 17–67.
T. K. Vinogradova and V. F. Dem'yanov, “On necessary conditions in minimax control problems,” Zh. Vychisl. Mat. Mat. Fiz.,14, No. 1, 233–236 (1974).
N. N. Vorob'ev, “Contemporary state of game theory,” Usp. Mat. Nauk,25, No. 2, 81–140 (1970).
N. N. Vorob'ev, Game Theory. Lectures for Economists-Cyberneticists [in Russian], Leningrad Univ. (1974).
R. Gabasov and F. M. Kirillova, Qualitative Theory of Optimal Processes [in Russian], Nauka, Moscow (1971).
R. Gabasov and F. M. Kirillova, Foundations of Dynamical Programming [in Russian], Belorussian State Univ., Minsk (1975).
R. Gabasov and F. M. Kirillova, “Methods of optimal controls,” in: Contemporary Problems of Mathematics [in Russian], Vol. 6 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1976), pp. 133–261.
M. S. Gabrielyan, “The problem of approach of a “group of controlled objects,” Izv. Akad. Nauk Arm.SSR, Mekh.,29, No. 3, 3–15 (1976).
M. S. Gabrielyan, “On the conflict problem of approach for group objects,” Uch. Zap. Erevan. Univ. Estestv. Nauk, No. 3(130), 23–30 (1975).
M. S. Gabrielyan, “On a game problem of guidance on a convex domain” Uch. Zap. Erevan. Univ. Estestv. Nauk, No. 1(131), 24–29 (1976).
M. S. Gabrielyan, “A stable game of pursuit for group objects,” Uch. Zap. Erevan. Univ. Estestv. Nauk, No. 2(135), 27–35 (1977).
Yu. B. Germeier, Introduction to the Theory of Operations Research [in Russian], Nauka, Moscow (1971).
Yu. B. Germeier, “On the combination of vector criteria of effectivity into one criterion,” in: Kinematics in the Service of Communism [in Russian], Vol. 6, Énergiya, Moscow (1971).
V. A. Gorelik and V. V. Fedorov, “On an approach to the solution of minimax problems of optimal control,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 1, 45–54 (1976).
V. V. Gorokhovik, “On a problem of vector optimization,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 6, 63–74 (1972).
V. V. Gorokhovik, “Some problems of vector optimization and differential games,” Author's Abstract of Candidate's Dissertation, Minsk Akad. Nauk BSSR (1973).
V. V. Gorokhovik, “Optimization problems with vector quality index,” in: Control and Optimization Problems [in Russian], Minsk (1976), pp. 134–147.
V. V. Gorokhovik, “Weak effectiveness conditions in finite-dimensional vector optimization problems,” Inst. Mat. Akad. Nauk BSSR, Preprint No. 12(12), Minsk (1976).
V. V. Gorokhovik, “Necessary conditions for weak effectiveness in a control problem with vector quality indices,” Inst. Mat. Akad. Nauk BSSR, Preprint No. 13(13), Minsk (1976).
V. V. Gorokhovik, “On necessary conditions for weak effectiveness in a control problem with vector quality indices,” Inst. Mat. Akad. Nauk BSSR, Preprint No. 4 (1978).
V. V. Gorokhovik and S. Ya. Gorokhovik, “Necessary conditions for optimality of singular controls in problems with fixed right end of a trajectory,” Dokl. Akad, Nauk BSSR,20, No. 3, 221–224 (1976).
V. V. Gorokhovik and F. M. Kirilova, “On scalarization of problems of vector optimization,” Dokl. Akad. Nauk BSSR, No. 7, 588–591 (1975).
V. V. Gorokhovik and M. P. Dymkov, “Optimization of linear systems according to vector criteria,” in: Differential and Integral Equations [in Russian], Vol. 3, Irkutsk (1975), pp. 245–256.
S. Ya. Gorokhovik, “Necessary conditions for optimality of multidimensional singular controls,” Differents. Uravn.,9, No. 9, 1721–1724 (1973).
S. Ya. Gorokhovik, “Necessary conditions for optimal in a problem with fixed right end of a trajectory,” Differents. Uravn.,11, No. 10, 1765–1773 (1975).
L. G. Gurin and E. M. Stolyarova, “The maximum principle in a minimax problem,” Zh. Vychisl. Mat. Mat. Fiz.,13, No. 5, 1175–1185 (1973).
V. N. Gurman and V. A. Dykhta, “Degenerate problems of optimal controls and the method of multiple maxima,” Avtom. Telemekh., No. 3, 51–59 (1977).
M. I. Gusev, “Vectorial optimization of linear systems,” Dokl. Akad. Nauk SSSR,207, No. 1, 21–24 (1972).
M. I. Gusev, “A controlled linear system optimizing vector criteria,” in: Extremal Strategies in Positional Differential Games [in Russian], Sverdlovsk (1974), pp. 77–104.
M. I. Gusev and A. B. Kurzhanskii, “On equilibrium situations in multicriterial game problems,” Dokl. Akad. Nauk SSSR,229, No. 6, 1295–1298 (1976).
P. B. Gusyatnikov, “Three-dimensional flight from many pursuers,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 5, 30–36 (1976).
P. B. Gusyatnikov, “Flight andl-flight in many-person differential games,” Dokl. Akad. Nauk SSSR,232, No. 3, 517–520 (1977).
P. B. Gusyatnikov and L. P. Yugai, “The flight problem in nonlinear differential games with terminal set of complex structure,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 2, 8–13 (1977).
N. N. Danilov, “The Pareto set in an n-person differential game with nonstrict competition,” in: Some Questions of Differential and Integral Equations and Their Applications [in Russian], Vol. 2, Yakutsk State Univ. (1977), pp. 25–35.
N. N. Danilov, “Structure of the Pareto set in a nonantagonistic differential game,” in: Questions of the Mechanics of Process Controls. Control of Dynamical Systems [in Russian], Vol. 2, Leningrad State Univ. (1978), pp. 44–50.
N. N. Danilov, “Stability of solutions in n-person differential games with terminal payoffs,” Fourth All-Union Conference on Game Theory, Abstracts, Gorki (1978), pp. 416–418.
N. N. Danilov, “Structure of the Pareto set in an n-person differential game,” Fourth All-Union Conference on Problems of the Theory of Cybernetics, Abstracts of Reports, Novosibirsk (1977), pp. 53–54.
Differential Games. Index of the Russian and Foreign Literature for 1968–1976 [in Russian], Izd. Akad. Nauk SSSR, Ural'skii Nauch. Tsentr., Sverdlovski (1978).
V. A. Dolodorenko and É. I. Fedan, “On a complex problem of optimal control of a multigoal system,” in: Complex Control Systems [in Russian] (1976), pp. 96–110.
A. Ya. Dubovitskii and A. A. Milyutin, “Extremal problems in the presence of restrictions,” Zh. Vyschisl. Mat. Mat. Fiz.,5, No. 3, 395–453 (1965).
M. P. Dymkov, “A method of construction of the set of unimprovable values of a functional in a problem of vector optimization,” in: Differential and Integral Equations [in Russian], Vol. 4, Irkutsk (1976), pp. 140–144.
S. V. Emel'yanov, V. I. Borisov, A. A. Malevich, and A. M. Cherkashin, “Models and methods of vector optimization,” in: Techniques of Cybernetics [in Russian], Vol. 5 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1973), pp. 386–448.
V. I. Zhukovskii, “On differential games of several persons with nonzero sum,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 3, 3–13 (1971).
V. I. Zhukovskii, “Optimality in a differential game of several persons,” in: Problems of Analytical Mechanics Theory of Stability and Control [in Russian], Nauka, Moscow (1975), pp. 143–147.
V. I. Zhukovskii and N. V. Stoyanov, “On the theory of certain differential games with time-lag,” Part I, Godishn. Vissh. Tekhn. Uchebn. Zaved., Mat.,9, No. 1, 7–21 (1973(1974)); Part II and Part III. Godishn. Vissh. Tekhn. Uchebn. Zaved., Mat.,9, No. 2, 9–41 (1973 (1974)).
V. I. Zhukovskii and N. V. Stoyanov, “On the pursuit problem with many participants,” Godishn. Vissh. Uchebn. Zaved., Prilozhen. Mat.,10, No. 3, 79–95 (1974 (1975)).
V. I. Zabotin, “Effectiveness conditions in problems of optimal control and nonlinear programming,” Author's Abstract of Candidate's Dissertation, Kazan Aviation Institute (1973).
V. I. Zabotin, “On some problems of optimization with collections of goal functions,” Tr. Kazan. Aviats. Inst., No. 147, 14–17 (1972).
V. I. Zabotin, “On an optimization problem with vector criteria,” Tr. Kazan. Aviats. Inst., No. 135, 69–75 (1971).
S. I. Zukhovskii, R. A. Polyak, and M. E. Primak, “On a concave n-person game and a production model,” Dokl. Akad. Nauk SSSR,191, No. 6, 1220–1223 (1970).
Indzuki Iosiiti, Nakamura Yukikhiro, “Study of probabilistic differential games,” Bull. Eng. Res. Inst. Kyoto Univ.,35, 34 (1969).
V. M. Ilyshev, “On the theory of optimal systems,” Kibernetika, No. 1, 122–124 (1972).
L. V. Kantorovich and V. L. Makarov, “Differential and functional equations arising in models of the dynamics of economics,” Sib. Mat. Zh.,11, No. 5, 1046–1059 (1970).
S. Karlin, Mathematical Methods in the Theory of Games, Programming, and Economics [Russian translation], Mir, Moscow (1964).
F. M. Kirillova and N. A. Poletaeva, “On some pursuit problems,” Abstracts of the International Congress of Mathematicians, Section 6, Nauka, Moscow (1966).
F. M. Kirillova, V. V. Gorokhovik, and M. N. Dymkov, “On the theory of vector optimization,” in: Materials of the All-Union Symposium on Optimal Controls and Differential Games, 1976 [in Russian], Metsniereba, Tbilisi (1977), pp. 139–145.
L. I. Kozhinskaya and L. I. Slutskii, “The role of the method of combination in vectorial optimization,” Avtom. Telemekh., No. 3, 167–170 (1973).
V. B. Kolmanovskii, “On some questions of optimal high speeds in stochastic systems,” Probl. Upr. Teorii Inf. (Vengr.),4, No. 4, 353–367 (1975).
V. B. Kolmanovskii, “On a problem of control of a gyrostat under random perturbations,” Avtom. Telemekh., No. 11 (1976).
I. A. Kornienko, “Some questions in the theory of operator minimax with applications to the problem of interorbital flight,” Author's Abstract of Candidate's Dissertation, Kazan Aviation Inst. (1974).
I. A. Kornienko, “Sufficient conditions for optimality of control with respect to a vector goal function and the choice of effective solutions,” Tr. Kazan. Aviats. Inst., No. 161, 55–60 (1974).
N. N. Krasovskii, Game Problems on Rendezvous of Trajectories [in Russian], Nauka, Moscow (1970).
N. N. Krasovskii and A. I. Subbotin, Postional Differential Games [in Russian], Nauka, Moscow (1974).
Yu. P. Krivenkov, “Necessary conditions for optimality for a linear problem of the mathematical theory of optimal processes with phase-restrictions,” Novosibirsk (1977).
A. B. Kurzhanskii, Control and Observation Under Conditions of Indeterminacy [in Russian], Nauka, Moscow (1977).
B. D. Lebedev, V. V. Podinovskii, and R. S. Styrikovich, “The problem of optimization with respect to an ordered collection of criteria,” Ekonomika Mat. Metody,7, No. 4, 612–616 (1971).
S. V. Lutmanov, “On an alternative in a differential game of several persons,” Prikl. Mat. Mekh.,41, No. 5, 813–818 (1977).
S. V. Lutmanov, “A theorem on an alternative for a k-person differential game,” Tr. Inst. Mat. Mekh. Uralsk. Nauch. Tsentr Akad. Nauk SSSR, No. 24, 68–76 (1977).
R. D. Lewis and H. Raifa, Games and Solutions [Russian translation], IL, Moscow (1961).
A. N. Maksimov and E. F. Filaretov, “The use of quadratic quality criteria for complex systems,” Izv. Vyssh. Uchebn. Zaved., Str., No. 9, 61–65 (1976).
V. P. Malyukov, “Conflicting interactions of economics in the framework of Leont'ev's model with incomplete information,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 5, 3–10 (1974).
V. M. Marchenko, “Group controllability of dynamical systems,” Vestn. Belorus. Univ., Ser. 1, No. 3, 72–73 (1974).
E. P. Maslov and V. N. Kharchev, “On the comparison of mean-square optimal and optimal strategies of pursuit,” Avtom. Telemekh.,5, 5–13 (1973).
B. S. Metev and I. P. Popchev, “A method of solution of a problem of group choice using metric space relations,” Avtom. Telemekh., No. 2, 81–87 (1977).
D. G. Metreveli, “Necessary and sufficient conditions for effectiveness in vector optimization problems,” Soobshch. Akad. Nauk Gruz.SSR,83, No. 3, 585–588 (1976).
D. G. Metreveli, “On a class of vector optimization problems,” Soobshch. Akad. Nauk Gruz.SSR,84, No. 3, 581–584 (1976).
D. G. Metreveli, “Necessary conditions for optimality in a control problem with vector quality criteria,” Abstracts of Reports of the First Conference of Young Students of Transcaucasia on Automatic Controls, Tbilisi (1977), pp. 3–6.
D. G. Metreveli, “On a vector optimization problem,” Tr. Inst. Sistem. Upr. Akad. Nauk Gruz. SSR,15, No. 1, 94–104 (1976).
B. G. Mirkin, The Problem of Group Choice [in Russian], Nauka, Moscow (1974).
E. F. Mishchenko, M. S. Nikol'skii, and N. Yu. Satimov, “The problem of deviation from rendezvous in many-person differential games,” Tr. Mosk. Inst. Akad. Nauk,143, 105–128 (1977).
E. F. Mishchenko and N. Yu. Satimov, “The problem of deviation from rendezvous in many-person differential games,” in: Materials of the All-Union Symposium on Optimal Controls and Differential Games [in Russian], Metsniereba, Tbilisi (1977), pp. 214–215.
V. S. Molostvov, “Some game problems in systems subjected to random influences,” Author's Abstract of Candidate's Dissertation, Moscow State Univ. (1974).
V. S. Molostvov, “Pareto optimality in some differential games,” Vestn. Mosk. Univ., Mat., Mekh., No. 2, 91–96 (1974).
V. S. Molostvov, “On Pareto strategies in some differential stochastic several-person games,” in: Problems of Analytical Mechanics the Theory of Stability and Controls [in Russian], Nauka, Moscow (1975), pp. 217–221.
V. S. Molostvov and Z. Varga, “Generalized solution of differential games with vector pentalities,” Abstracts of the Fourth All-Union Meeting on Statistical Methods in Control Theory [in Russian], Frunze (1978), pp. 84–85.
V. D. Nogin, “On a vector optimization problem of multistage processes of adoption of a solution,” in: Dynamical Modeling of the Processes of Adoption of Solutions [in Russian], Vladivostok (1976), pp. 111–116.
V. D. Nogin, “A new method of restriction of the domain of compromises,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 5, 10–14 (1976).
V. D. Nogin, “On a problem of multigoal controls,” Abstracts of Reports of the All-Union Conference on the Qualitative Theory of Differential Equations [in Russian], Ryazan (1976), pp. 218–219.
I. F. Ogorodneichuk, E. G. Kunik, A. Ya. Kuzemin, A. G. Osinevskii, and L. A. Golovko, “Methods of multicriterial optimization,” in: Instruments and Automatic Systems [in Russian], Resp. Mezhved. Temat. Nauchno-Tekh. Sb.,27 (1973), pp. 43–54.
L. A. Petrosyan, “Differential games of pursuit,” Author's Abstract of Doctoral Dissertation, Leningrad State Univ. (1971).
L. A. Petrosyan, “Pursuit games with ‘lifelines’ with many participants,” Izv. Akad. Nauk Arm. SSR (Mat.),1, No. 5, 331–340 (1966).
L. A. Petrosyan, “Differential survival games with many participants,” Dokl. Akad. Nauk SSSR,161, No. 2, 285–287 (1965).
L. A. Petrosyan, “Stability of solutions in differential games with many participants,” Vestn. Leningr. Univ., No. 19, 46–52 (1977).
L. A. Petrosyan, “Nonantagonistic differential games,” in: Questions of the Mechanics of Control Processes. Control by Dynamical Systems [in Russian], Vol. 2, Leningr. Univ. (1978), pp. 173–181.
L. A. Petrosyan and N. V. Murzov, “Contract games with many participants,” Vestn. Leningr. Univ.,3, No. 13, 125–129 (1967).
L. A. Petrosyan, “Game-theoretic problems of mechanics,” Lit. Mat. Sb.,6, No. 3, 423–433 (1966).
L. I. Plotnikova, “Some problems of optimal interaction of several controlled objects,” Candidate's Dissertation, Novosibirsk (1972).
L. I. Plotnikova, “On a problem of optimal control. Controlled Systems,” Novosibirsk,6, 36–43 (1970).
L. I. Plotnikova, “Numerical solution of a problem of search for a rendezvous point of several controlled objects,” in: Tr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR,8, 39–42 (1971).
V. V. Podinovskii, “Multicriterial problems with uniform equivalent criteria,” Zh. Vychisl. Mat. Mat. Fiz.,15, No. 2, 330–344 (1975).
V. V. Podinovskii, Methods of Multicriterial Optimization [in Russian], Tr. VIA im. Dzerzhinskogo, Moscow (1971).
V. V. Podinovskii, “Application of the procedure of maximization of a basic local criterion for solving problems of the theory of vectorial optimization,” in: Controlled Systems [in Russian], Vol. 6, Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1970), pp. 17–22.
V. V. Podinovskii, “Effective sequences and their properties,” in: Mathematical Methods in the Social Sciences [in Russian], Vol. 2, Vilnius (1972), pp. 75–88.
V. V. Podinovskii and V. M. Gavrilov, Optimization with Respect to Successively Applied Criteria [in Russian], Sovet-skoe Radio, Moscow (1975), Chap. 4.
L. S. Pontryagin, “On the theory of differential games,” Usp. Mat. Nauk,21, No. 4, 219–274 (1966).
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).
U. K. Prasad and N. D. Sarma, “Multicriterial problems of optimal control: Nash-Kharsan' game cooperative solutions,” Avtom. Telemekh., No. 6, 95–105 (1975).
N. V. Prodan and I. S. Chebotaru, “On necessary conditions for optimality in games with nonopposite and opposite interests,” in: Studies in Algebra, Mathematical Analysis, and Their Applications. Mathematical Sciences [in Russian], Kishinev (1977), pp. 104–109.
B. N. Pshenichnyi, “Simple pursuit by several objects,” Kibernetika, No. 3, 145–146 (1976).
A. E. Radievskii, “On the existence of solutions of multicriterial synthesis for linear control objects,” in: Sistemy Prom. Kibern. [in Russian], Kiev (1975), pp. 28–32.
B. B. Rikhsiev, “Sufficient conditions for a class of many-person differential games,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 69–70 (1977).
V. E. Ryzhova, “Some problems of control of motion with parametrically given control actions,” Candidate's Dissertation, Moscow State Univ. (1976).
V. E. Ryzhova, “On a problem of control with two criteria,” Nauch. Tr. Inst. Mekh., Mosk. Univ., No. 40, 30–47 (1975).
V. E. Ryzhova, “On a problem of vectorial optimization,” Vestn. Mosk. Univ., Mat., Mekh., No. 4, 119–123 (1976).
M. E. Salukvadze, Problems of Vectorial Optimization in the Theory of Controls [in Russian], Metsniereba, Tbilisi (1975).
M. E. Salukvadze, “On optimization of vector functionals 1, Programmed optimal trajectories. II,” Avtom. Telemekh., No. 8, 5–15 (1971); No. 9, 5–15 (1971).
M. E. Salukvadze, “Vector functionals in linear problems of analytic construction,” Avtom. Telemekh., No. 7, 5–12 (1973).
V. K. Sivtsova, “Application of an integral minimax principle to solve nonsmooth problems of optimal control,” Abstracts of Reports of the Third All-Union Conference on Operations Research, Gorki (1978), pp. 342–343.
S. L. Skerus, “Some coalitional differential games,” Author's Abstract of Candidate's Dissertation, Vilnius State Univ. (1973).
S. L. Skerus and I. P. Yachauskas, “Three-person coalitional differential games,” Lit. Mat. Sb.,11, No. 4, 887–898 (1971); Second All-Union Conference on Game Theory. Abstracts of Reports, Vilnius (1971), pp. 103–105; in: Progress in Game Theory [in Russian], Vilnius (1973), p. 235.
S. L. Skerus and I. P. Yachauskas, “A coalitional n-person game,” Lit. Mat. Sb.,13, No. 2, 163–175 (1973).
S. L. Skerus and I. P. Yachauskas, “A coalitional linear differential game,” in: Mathematical Methods in the Social Sciences [in Russian], Vol. 4, Vilnius (1974), pp. 57–68.
S. L. Skerus and I. P. Yachauskas, “On a cooperative differential game,” Abstracts of the Third All-Union Conference on Game Theory, Odessa (1974), pp. 66–67.
T. V. Slobodinskaya and L. A. Petrosyan, “Simultaneous pursuit games,” in: Mathematical Methods in the Social Sciences [in Russian], Vol. 5, Vilnius (1975), pp. 23–36.
É. R. Smol'yakov, “The concept of solution of an N-person coalitional game with transferability,” Dokl. Akad. Nauk SSSR,210, No. 6, 1290–1292 (1973).
T. Tanabe, “On the choice of an optimal variant of rendezvous with several goals,” in: Control in Space [in Russian], Vol. 2, Nauka, Moscow (1975), pp. 83–94.
T. A. Tadumadze, “Extremal problems with variable lags, characterized by multidimensional quality criteria,” SakartevelosSSR Metsnierebata Akademia Martvis Sistemebis Instituti Shromebi, Tr. Inst. Sistem Upr. Akad. Nauk Gruz. SSR,13, No. 1, 5–28 (1974).
T. A. Tadumadze, “Maximum principle for certain controlled systems of neutral type,” Annotatsii Dokl. Sem. Inst. Prikl. Matm., Tbiliskogo Univ., No. 9, 9–13 (1974).
S. I. Tarlinskii, “On a linear differential game of approach of several controlled objects,” Dokl. Akad. Nauk SSSR,230, No. 3, 534–537 (1976).
N. T. Tynyanskii, “Studies in the theory of duality of nonlinear programming and differential games,” Author's Abstract of Doctoral Dissertation, VTs Akad. Nauk SSSR, Moscow (1969).
N. T. Tynyanskii and V. I. Zhukovskii, “Differential games with nonzero sum (coalition-free variant),” Itogi Nauki i Tekh. VINITI. Ser. Mat. Anal., Moscow,15, 199–266 (1977).
A. M. Formal'skii, “Minimization of impulse and a problem of optimal control with two functionals,” Nauch. Tr. Inst. Mekh. Mosk. Univ., No. 40, 5–29 (1975).
V. D. Furasov, Stability of Motion, Estimates and Stabilization [in Russian], Nauka, Moscow (1977).
V. V. Khomenyuk, Optimal Systems of Control [in Russian], Nauka, Moscow (1977).
I. S. Chebotaru, É. S. Naval, and M. I. Sagaidak, “The maximum principle for an optimal problem,” in: Applications of Mathematics and Programming [in Russian], Vol. 12, Kishinev (1974), pp. 95–103.
F. L. Chernous'ko and V. B. Kolmanovskii, Optimal Controls for Random Perturbations [in Russian], Nauka, Moscow (1978).
F. L. Chernous'ko and V. B. Kolmanovskii, “Numerical and approximation methods of optimal control,” Itogi Nauki i Tekh. Mat., Analiz. VINITI Akad. Nauk SSSR,14, 101–166 (1977).
F. L. Chernous'ko and A. A. Melikyan, Game Problems of Control and Search [in Russian], Nauka, Moscow (1976).
A. A. Chikrii, “On a method of escape from several pursuers,” Avtom. Telemekh.,8, 33–37 (1978).
A. A. Chikrii, “Sufficient conditions for escape in nonlinear differential games of several persons,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 6, 22–29 (1978).
A. A. Chikrii, “Pursuit by several controlled objects of an escapee with delay of information on the state of the pursuers,” Preprint Inst. IK Akad. Nauk Ukr. SSR, No. 45, 23–30 (1978).
A. A. Chikrii and I. S. Rappoport, “Problem of approach in a differential game of several persons,” Preprint Inst. Kibern. Akad. Nauk Ukr. SSR, No. 88 (1977).
A. A. Chikrii and I. S. Rappoport, “Linear differntial games of pursuit with the participation of several persons,” Dokl. Akadl Nauk Ukr. SSR, No. 6, 553–556 (1978).
S. V. Chistyakov, “On differential games of N-persons,” in: Mathematical Methods in the Social Sciences [in Russian], Vol. 8, Vilnius (1976), pp. 111–116.
N. P. Shvetsov, “Investigation of a hieratic group differential game,” in: Hieratic Dynamical Systems of Control [in Russian], Naukova Dumka, Kiev (1975), pp. 122–132 (SI Tekh. Kibern.,4, No. 21, 214 (1975).
A. Yu. Shevlyakov, “On a generalized Kalman-Busy equation,” in: Theory of Random Processes [in Russian], Vol. 3, Naukova Dumka, Kiev (1975), pp. 142–149.
Z. M. Shportyuk, “On solutions of a problem of deviation from rendezvous with a coalition of pursuers,” in: Scientific Conference on Computable Mathematics in Contemporary Scientific-Technical Progress [in Russian], Vol. 2, Kanev (1974), pp. 286–289.
K. Arrow, L. Hurwicz, and Kh. Udzawa, Investigation in Linear and Nonlinear Programming [Russian translation], IL, Moscow (1962).
E. B. Yanovskaya, “Optimality criteria in coalition-free games,” in: Progress in the Theory of Games [in Russian], Vilnius (1973), pp. 106–114.
M. Andjelic, “On a matrix Riccati equation of cooperative control,” Int. J. Control,23, No. 3, 427–432 (1976).
A. H. Andry, “Pareto optimality and systems governed by partial differential equations,” Proc. IEEE Conf. Decision and Control included in 15th Symposium on Adaptive Processes, Clearwater, Fla., 1976, New York (1976), pp. 107–110.
M. Aoki and M. T. Li, “Controllability and stabilizability of decentralized dynamic systems,” 14th Joint Automatic Controls Conference, Columbus, Ohio (1973), Preprint of Technical Papers, New York (1973), pp. 278–286.
M. Athans and H. P. Geering, “Necessary and sufficient conditions for differentiable nonscalar-valued functions to attain extrema,” IEEE Trans. Autom. Control,AC-18, No. 2, 132–139 (1973).
E. Bamba, “Constrained optimization under vector-valued performance index,” Systems Control,16, No. 5, 409–418 (1972).
T. Basar, “A new dynamic model for duopoly markets,” in: Proc. Eighth Princeton Conference on Information Sciences and Systems, March, 1974.
G. Basile and T. L. Vincent, “Absolutely cooperative solution for a linear multiplayer differential game,” J. Optimiz. Theory Appl.,6, No. 1, 41–46 (1970).
G. Basile and T. L. Vincent, “On the cooperative game,” Paper presented at the Third Hawaii International Conference on System Sciences, Honolulu, Hawaii (1970).
K. Bergstresser and P. L. Yu, “Domination structures and multicriteria problems in n-person games,” Theory Decision,8, No. 1, 5–48 (1977).
L. J. Billera, “Some recent results in n-person game theory,” Technical Report No. 124, Dept. of Operations Research, Cornell University, Ithaca (1970).
A. Blaquière, “Sur la geometrie des surfaces de Pareto d'un jeu différentiel a N joueres,” C. R. Acad. Sci.,271, No. 15, A744-A746 (1970).
A. Blaquière, Topics in Differential Games, North-Holland, Amsterdam-London, Elsevier, New York (1973).
A. Blaquière and P. Caussin, “Jeux différentiels avec retard, propriétes globales d'une surface du jeu,” C. R. Acad. Sci.,273, No. 5, A326-A328 (1971).
A. Blaquière, “Further topological aspects of vector-valued optimization in multilayer quantitative games,” Proc. IEEE Conference on Decision and Control, 13th Symposium on Adaptive Processes, Phoenix, Arizona, 1974, New York (1974), pp. 373–374.
A. Blaquière and K. E. Wiese, “Some geometric aspects of Pareto surfaces of an n-player differential game,” Proceedings of 4th Hawaii International Conference on Systems Science, Honolulu, Hawaii, 1971, North Hollywood, California (1971), pp. 27–29.
A. Blaquière and K. Wiese, “Jeux qualitatifs multiétages a N-personnes coalitions,” C. R. Acad. Sci.,270, No. 19, A1280-A1282 (1970).
A. Blaquière, K. Wiese, and L. Juricek, “Sur la géométrie des surfaces de Pareto d'un jeu differentiel á N-joueurs, théoréme du maximum,” C. R. Acad. Sci.,A271, No. 20, A1030-A1032 (1970).
A. Blaquière, K. Wiese, and L. Juricek, “Some geometric aspects of Pareto surfaces of an N-player differential game,” in: Proceedings of the Fourth Hawaii International Conference on Systems Science, Honolulu, Hawaii, 1971, North Hollywood, California (1971), pp. 27–29.
A. Blaquière, K. Wiese, and L. Juricek, “Geometry of Pareto equilibria and maximum principle in N-person differential games,” J. Math. Anal. Appl.,38, No. 1, 223–243 (1972).
A. Blaquière, K. Wiese, and L. Juricek, “Geometry of Pareto equilibria in N-person differential games,” in: Topics in Differential Games, New York (1973), pp. 271–310.
A. Blaquière and L. Juricek, “Appendix — an example of duopoly,” in: Differential Games and Related Topics, New York (1971), pp. 74–81.
J. Bonnardeaux, J.-P. Dolait, and J. S. Dyer, “The use of the Nash bargaining model in trajectory selection,” Manag. Sci.,22, No. 7, 766–777 (1976).
J. Bradley and P. L. Yu, “A concept of optimality in differential games,” Int. J. Syst. Sci.,7, No. 2, 157–164 (1976).
G. Bühler, “Die Optimalitätsgleichung bei mehrstufigen Spielen und ihre Lösbarkeit,” Oper. Res.-Verfahren, Vol. 16, Meisenheim (1973), pp. 68–83.
G. Bühler, “Zur Theorie dynamischer nichtcooperativer zwei Personspiele,” Z. Operat. Res.,A-17, No. 3, 143–156 (1973).
J. Case, “Applications of the theory of differential games to economic problems,” in:Differential Games and Related Topics, H. W. Kuhn and G. P. Szego (editors), Elsevier, New York (1971), pp. 345–371.
J. Case, “On some differential games in economics,” MRC Report, No. 874 (1968).
J. Case, “Differential trading games,” in: Topics in Differential Games, New York (1973), pp. 377–400.
J. Case, “A game of advertising strategy,” Proc. IFAC 6th World Congress, Boston-Cambridge, Mass., 1975, Part 1, Pittsburg (1975), 16.3/1–16.3/3.
J. Case, “A problem in international trade,” Proc. First International Conference on the Theory and Applications of Differential Games, Amherst. Mass., 1969, S. 1. s.a. IV/8–IV/12.
J. Case, “Impulsively controlled differential games,” in: Theory and Applications of Differential Games, Dodrecht-Boston (1975), pp. 179–187.
J. Case, “A class of games having Pareto optimal Nash equilibria,” J. Optimiz. Theory Applications,13, No. 3, 379–385 (1974).
L. Cesari and M. B. Suryanarayana, “Existence theorems for Pareto optimization in Banach spaces,” Bull. Am. Math. Soc.,82, No. 2, 306–308 (1976).
S. S. L. Chang, “General theory of optimal processes,” SIAM J. Control, No. 4, 46–55 (1966).
A. Charnes and W. Cooper, Management Models and Industrial Applications of Linear Programming, No. 5, Wiley (1961).
A. Charnes and W. Cooper, “Goal programming and multiple objective optimization. I,” J. Operational Res.,1, No. 1 (1977).
Kai-Ching Chu, “On the noninferior set for the systems with vector-valued objective function,” IEEE Trans. Autom. Control,AC-15, No. 5 (1970).
D. H. Chyung, “Optimal systems with multiple cost functionals,” SIAM J. Control,5, No. 3, 345–350 (1967).
D. H. Chyung, “Time-optimal rendezvous of three linear systems,” J. Optimiz. Theory Appl.,12, No. 3, 242–247 (1973).
S. Clemhout, H. Y. Wan, and G. Leitmann, “A model bargaining under strike the differential game,” View Control Working Paper in Economics, No. 66 (1973).
S. Clemhout, H. Y. Wan, and G. Leitmann, “A differential game of Oligopoly,” Kybernetika,3, No. 1, 24–39 (1973).
S. Clemhout, H. Y. Wan, and G. Leitmann, “Equilibrium patterns for bargaining under strike a differential game model,” in: Proceedings of the Conference on Direction in Decentralized Control, Many Person Optimization, and Large Scale Systems, Plenum Press (1976).
S. Clemhout, H. Y. Wan, and G. Leitmann, “A differential game model of duopoly,” Econometrica,39, No. 6, 911–938 (1971).
S. Clemhout, H. Y. Wan, and G. Leitmann, “Bargaining under strike: a differential game view,” J. Econ. Theory,11, No. 1, 55–67 (1975).
S. Clemhout, H. Y. Wan, and G. Leitmann, “Equilibrium patterns for bargaining under strike a differential game model,” Proc. IFAC 6th World Congress, Boston-Cambridge, Mass., 1975, Part I, Pittsburg, Pa., 1975, 16.5/1–16.5/12.
N. O. da Cunha, “Constrained minimization under vector-valued criteria,” Doctoral Dissertation, Berkley, University of California (1966).
N. O. da Cunha and E. Polak, “Constrained minimization under vector-valued criteria in finite dimensional spaces,” J. Math. Anal. Appl.,19, No. 1, 103–124 (1967).
N. O. da Cunha and E. Polak, “Constrained minimization under vector-valued criteria in linear topological spaces,” in: Math. Theory Control, Academic Press, New York-London (1967), pp. 96–108.
E. P. Cunningham, “The absolute maximum payoff in differential games and optimal control,” J. Optimiz. Theory Appl.,7, No. 4, 248–256 (1971).
E. P. Cunningham, “Differential games with absolute maximum payoff,” Proceedings of the First International Conference on the Theory and Applications of Differential Games, Mass., 1969, S. 1, s.a., III/16–III/17.
P. C. Das and R. R. Sharma, “On optical controls with vector-valued cost functionals,” Rev. Roum. Math. Pures Appl.,16, No. 3, 341–354 (1971).
G. de Menil, “Bargaining; Monopoly power versus union power,” MIT Press, Cambridge, Mass. and London, 1971, Int. J. Game Theory,2, No. 3, 204 (1973).
M. C. Delfour and S. K. Mitter, “Control of hereditary differential systems,” Proc. IFAC 5th World Congress, 1972, Part 4, S. 1., s.a., 36-1/1–36-1/8.
H. W. Kuhn and G. R. Szegö (ed.), Differential Games and Related Topics, North-Holland, Amsterdam (1971).
J. Doležal, “Some properties of nonzero-sum multistage games,” Lect. Notes Comput. Sci.,27, 451–459 (1975).
J. Doležal, “Existence of optimal in general discrete systems,” Kybernetika,1, No. 4, 301–312 (1975).
J. Doležal, “Necessary optimality conditions for N-player nonzerosum multistage games,” Kybernetika,12, No. 4, 268–295 (1976).
C. Dragusin, “Penalty functions in vectorial-optimization criteria,” Bull. Univ. Brason, Sec. C, Mat. Fiz. Chim. Sci. Natur.,16, 25–34 (1974).
N. P. Dwivedi, “Deterministic optimal maneuver strategy for multitarget missions,” J. Optimiz. Theory Appl.,17, No. 1–2, 133–153 (1975).
R. Farquhavson, “Sur une gènéralisation de la notion d'équilibrium,” C. R. Acad. Sci. Paris,240, No. 1, 46–48 (1955).
F. D. Faulkner, “On finding solutions which dominate equilibrium solutions to some N-person differential games,” Lect. Notes Econ. Math. Syst.,106, 155–167 (1974).
P. S. Fishburn, “A study of independence in multivariate utility theory,” Econometrica,37, No. 1 (1969).
M. Freimer and P. L. Yu, “Some new results on compromise solutions for group decision problems,” Manage. Sci.,22, No. 6, 688–693 (1976).
H. P. Geering, “Optimal control theory for non-scalar-valued performance criteria,” Ph. D. Dissertation, Dept. Electr. Eng. MIT, Cambridge (1971).
H. P. Geering and M. Athans, “The infimum principle,” Proc. IEEE Conf. Decision and Control included in 12th Symposium on Adaptive Processes, San Diego, Calif., 1973, New York, 1973, pp. 577–593, IEEE Trans. Autom. Control,19, No. 5, 485–494 (1974).
H. P. Geering and M. Athans, “Optimal control theory for nonscalar-valued performance criteria,” Proc. 5th Annual Princeton Conference on Information Sciences and Systems, 1971. Princeton, s.a. 479–483.
A. M. Geoffrion, “Proper efficiency and the theory of vector maximization,” J. Math. Anal. Appl.,22, No. 3, 618–630 (1968).
V. B. Gindes, “A problem of optimal joint control,” SIAM J. Control,5, No. 2, 222–227 (1967).
V. V. Gorohovik, “The optimization of systems with vector-valued objective functions,” Multivar. Technol. Syst. Proc. Symp. Manchester, 1974, London (1975), S 32-1–S 32-4.
V. Gourishankar and A. Salama, “A technique for solving a class of differential games,” Int. J. Control,15, No. 3, 529–539 (1972).
Yu. P. Gouskov, “Automatic landing as a terminal control problem,” Proc. IFAC 5th World Congr., Paris, 1972, Part 2, Pittsburgh (1971), 19,2/1–19,2/6.
J. D. Grote, “Dynamics of cooperative games,” Int. J. Games Theory,5, No. 1, 27–64 (1976).
J. D. Grote, “Solution sets for N-person games,” in: Theory and Appl. Differential Games, Dordrecht-Boston (1975), pp. 63–75.
P. Hageborn, “Ein Differentialspiel mit zwei Verfolgern und einem Verfolgten,” Z. Angew. Math. Mech.,56, no. 3, Sonderh, 342–345 (1976).
P. Hageborn and J. V. Breakwell, “A differential game with two pursuers and one evader,” J. Optimiz. Theory Appl.,18, No. 1 15–29 (1976). Muliciber Decis. Mak. and Differ. Games, New York-London (1976), pp. 443–457.
A. Haurie, “Jeux quantitatifs multiétages a N-joueurs equilibries de Nash, Pareto-optimalité, C-optimalité,” Rev. CETHEDEC,9, No. 30, 83–108 (1972).
A. Haurie, “On Pareto optimal decisions for a coalition of subset of players,” IEEE Trans. Autom. Control,AC-18, No. 2, 144–149 (1973).
A. Haurie, “Optimalite dans un système multicritère et perturbe avec application à des systèmes de commande linéaires à couts quadratiques,” Ref. Franc. Automat. Inform. Rech. Oper.,7, No. R-2, 91–105 (1973).
A. Haurie, “Jeux quantitatifs a M-joueurs,” Doctoral Dissertation, Paris (1970).
A. Haurie, “A note on nonzero-sum differential games with bargaining solution,” J. Optimiz. Theory Appl.,18, No. 1, 31–39 (1976).
A. Haurie and I. L. Goffin, “Necessary conditions and sufficient conditions for Paretooptimality in a Multicriterion perturbed system,” Proc. 5th IFIP Conference on Optimization Techniques, Rome, 1973.
A. Haurie and M. C. Deflour, “Individual and collective rationality in a dynamic Pareto equilibrium,” J. Optimiz. Theory Appl.,13, No. 3, 290–302 (1974).
M. Hisashi and S. Harunori, “A method of determining characteristic functions for cooperative differential games without side payment,” Mem. Fac. Eng. Kyoto Univ.,38, No. 4, 169–181 (1976).
Y. C. Ho, “Differential games, dynamic optimization, and generalized control theory,” J. Optimiz. Theory Appl.,6, No. 3, 179–209 (1976).
Y. C. Ho, “Comment on a paper by J. Medanic and M. Andjelic,” J. Optimiz. Theory Appl.,10, No. 3, 187–189 (1972).
S. C. Huang, “Note on the mean-square strategy-for vector-valued objective functions,” J. Optimiz. Theory Appl.,9, No. 5, 364–366 (1972).
S. C. Huang, “Optimal control problems with vector-valued criterion function,” IEEE Conference on Decis. and Contr. (Incl. 10th Symp. Adapt. Process), Miami Beach, 1971. New York (1971), pp. 462–463.
G. P. Huber, “Multiattribute utility models: a review of field and fieldlike studies,” Manage. Sci.,20, No. 10, 1393–1402 (1974).
L. Juricek, “Games with coalition,” in: Topics in Differential Games, New York (1973), pp. 311–344.
L. Juricek, “Jeux differentiels à N-joueurs cooperatifs et non cooperatifs,” Thèse doct. sci., Univ. Paris (1972).
L. Juricek and K. Wiese, “Sur la gèomètrie des surfaces de Pareto d'un jeux differentiel à N-joueurs; theoreme du maximum,” C. R. Acad. Sci.,A271, No. 20, 1030–1032 (1970).
S. J. Kahne, “Optimal cooperative state rendezvous and Pontryagin's maximum principle,” Int. J. Control,2, No. 5, 425–431 (1965).
E. Kalai, “Excess functions for cooperative games without side-payments,” SIAM J. Appl. Math.,29, No. 1, 60–71 (1975).
Tamura Katsutoshi, “Linear optimal problems with a vector-valued performance index,” Trans. Soc. Instrum. Control Eng.,10, No. 6, 749–755 (1974).
H. J. Kimura, Soc. Instrum. Control Eng.,10, No. 9, 637–660 (1971).
A. Klinder, “Vector-valued performance criteria,” IEEE Trans. Autom. Control,AC-9, No. 1, 117–118 (1964).
Toshiro Kobayashi and Yoshikazu Sawaragi, “Distributed parameter differential games,” Syst. Control,18, No. 2, 101–111 (1974).
A. J. Koivo, “On a differential game with three players,” Proc. Int. Conf. Theory and Appl. Differential Games, Amherst, Mass. 1969, s.1, s.a. VIII/18–VIII/19.
A. J. Koivo and D. W. Repperberger, “Optimization of terminal rendezvous as a cooperative game,” 12th Joint Automatic Control Conference of the American Automatic Controls Council, St. Louis, Mo., 1971, Prepr.techn. pap., New York (1971), pp. 508–516.
O. Kolbe and P. Sagirow, “Ein optimales Rendezvous zweier aktiver Flugkörper,” Z. Angew. Math. Mech.,48, 8, Sonderh., 269–271 (1968).
N. J. Kirikelis, “A linearization method in N-person nonzero-sum differential games,” J. Optimiz. Theory Appl.,9, No. 5, 359–363 (1972).
N. J. Krikelis and Z. V. Rekasius, “On the solution of the optimal linear control problems under conflict of interest,” IEEE Trans. Autom. Control,16, No. 2, 140–147 (1971).
A. B. Kurzhanskii and M. I. Gusev, “On multicriteria solutions in game-theoretic problems of control,” IIASA Workshop on Decision Making with Multiple Objectives, Vienna, 1975, 2, 51–67.
B. Kyrtavan, “Dynamic two-person two-objective control problems with delayed sharing information pattern,” IEEE Trans. Autom. Control,22, No. 4, 659–661 (1977).
B. Lantos, “Necessary conditions for the optimallty in optimum control problem with nonscalar-valued performance criterion,” in: Problems of Control and Information Theory, No. 3, 1033–1040 (1976).
J. J. Lawser and R. A. Volz, “A nonzero-sum differential game with curious solution properties,” IEEE Trans. Autom. Control,17, No. 5, 717–718 (1972).
J. J. Lawser and R. A. Volz, “Some aspects of nonzero-sum differential games,” IEEE Trans. Autom. Control,16, No. 1, 66–69 (1971); Proc. First International Conference on the Theory and Applications of Differential Games, Amherst, Mass., 1969, S.1., s.a., IV/ 19–IV/22.
A. L. Leatham and G. M. Anderson, “A class of nonzero-sum differential games with open-loop,” Proc. 4th Haw. Int. Conf. Syst. Sci., Honolulu, Hawaii, 1971. North Hollywood, Calif. (1971), pp. 199–241.
G. Leitmann, Cooperative and Noncooperative Many Players Differential Games, Springer-Verlag, Vienna (1974).
G. Leitmann, “Many player differential games,” Proc. of Workshop of Differential Games. Twente Univ., Enschede, Holland, Springer-Verlag (1977).
G. Leitmann, “Collective bargaining: a differential game,” J. Optimiz. Theory Appl.,11, No. 4, 405–412 (1973).
G. Leitmann, “Cooperative and noncooperative differential games,” in: Theory and Applications of Differential Games, Dordrecht-Boston (1975), pp. 85–96.
G. Leitmann and P. T. Liu, “A differential game model of labor-management negotiation during a strike,” J. Optimiz. Theory Appl.,13, No. 4, 427–435 (1974).
G. Leitmann and P. T. Liu, “A differential game model of labor-management negotation during a strike,” J. Optimiz. Theory Appl.,14, No. 4, 443–444 (1974).
G. Leitmann and S. Rocksin, “The effect of playbility in differential games on the relation between best guaranteed costs and saddlepoint values,” J. Optimiz. Theory Appl.,15, 509–516 (1975).
G. Leitmann, S. Rocksin, and T. Vinsent, “A note on control space properties of cooperative games,” J. Optimiz. Theory Appl.,9, No. 6, 379–390 (1972).
G. Leitmann and W. Schmitendorf, “Some sufficiency conditions for Paretooptimal control,” 13th Joint Autom. Contr. Conf. Am. Automat. Contr. Counc., Stanford, Calif., 1972. Prepr. Techn. Pap. New York, 1972, 1–7.
G. Leitmann and P. L. Yu, “Compromise solutions, domination structures and Salukvadze's solution,” J. Optimiz. Theory Appl.,13, No. 3, 362–378 (1974).
G. Leitmann and P. L. Yu, “Nondominated decisions and cone convexity in dynamic multicriteria decision problems,” J. Optimiz. Theory Appl.,14, No. 5, 573–584 (1974).
G. Leitmann and W. Stadler, “Cooperative games for the experimentalist,” Zag. drgan nielin.,15, 273–285 (1974).
P. Levine, “Strategic ‘prejndsments’ and decision criteria in N-person games,” in: Theory and Application Differential Games, Dordrecht-Boston (1975), pp. 121–132.
J. G. Lin, “Proper equality constraints and maximization on index vectors,” J. Optimiz. Theory Appl.,20, No. 2, 215–244 (1976).
Pan-Tai Liu, “Optimal threat strategies in differential games,” J. Math. Anal. App.,43, No. 1, 161–169 (1973).
Pan-Tai Liu, “Nonzero-sum differential games with bargaining solutions,” J. Optimiz. Theory Appl.,11, No. 3, 284–292 (1973).
W. F. Lucas, “Some recent developments in n-person game theory,” SIAM Rev.,13, No. 4, 491–523 (1971).
W. F. Lucas, “An overview of the mathematical theory of games,” Manag. Sci.,18, No. 5, part 2, 3–19 (1972).
W. F. Lucas, “A game with no solution,” Bull. Am. Soc.,74, No. 2, 237–239 (1968).
E. Marchi, “E-points of games,” Proc. Nat. Acad. Sci. USA,57, No. 4, 878–882 (1967).
E. Marchi, “A class of games that evolve,” Z. Wahr. Verw. Geb.,18, No. 4, 271–280 (1971).
L. Markus, “Catastrophe theory in differential games,” in: Theory and Applications of Differential Games, Dordrecht-Boston (1975), pp. 301–310.
J. Medanic and M. Andjelić, “Minimax solution of the multiple-target problem,” IEEE Trans. Autom. Control,17, No. 5, 597–604 (1972).
J. Medanic and M. Andjelić, “On a class of differential games without saddlepoint solutions,” J. Optimiz. Theory Appl.,8, No. 6, 413–430 (1971).
J. Medanic and M. Andjelić, “Convex approximation of the solution of the matrix Riccati equation,” IEEE Trans. Autom. Control,20, No. 2, 234–238 (1975).
Meski Muncer, “A new approach to the ‘inverse problem of optimal control theory’ by generalized performance index (GPI),” 14th J. Autom. Control Conf., Columbus, Ohio, 1973, Prepr. Tech. pap. New York, 1973, pp. 686–691.
P. Michel, “Condition nécessaire d'optimalité de Pareto pour un systéme á commande,” C. R. Acad. Sci.,280, A1397–1399 (1975).
Multicriteria Decision Making and Differential Games, G. Leitmann (ed.), Plenum Press, New York-London (1976).
R. Muralidharan and Y. C. Ho, “A piecewise-closed formalgorithm for a family of minimax and vector criteria problems,” IEEE Trans. Autom. Control,20, No. 3, 381–385 (1975).
J. Nash, “Two-person cooperative games,” Econometrica,21, 128–140 (1953).
W. L. Nelson, “On the use of Optimization Theory for practical control system design,” IEEE Trans. Autom. Control,AC-9, No. 4, 469–477 (1964).
L. W. Neustadt, “A general theory of extremals,” J. Comput. Syst. Sci., No. 3, 57–92 (1969).
G. Olech, “Existence theorems for optimal problems with vector-valued cost function,” Trans. Am. Math. Soc.,136, 159–180 (1969).
V. Pareto, Course d'Economie Politique, Lauranue, Rouge (1896).
M. Philippe, “Condition nécessaire d'optimalité de Pareto pour un système á commande,” C. R. Acad. Sci.,280, No. 20, A1397-A1399 (1975).
R. Perez and C. C. Li, “Performance sensitivity of linear quadratic two-person differential games,” Proc. 5th Annu. Princeton Conference on Inform. Sci. and Syst., 1971, Princeton, New Jersey, s.a., 486.
K. Pitter, “Optimization theory in linear spaces. I,” Math. Ann.,182, 182 (1969); II. Math. Ann.,183, 200 (1969); III. Math. Ann.,184, 133 (1969).
S. R. Plisha, “Multiperson controlled diffusions,” SIAM J. Control,11, No. 4, 563–586 (1973).
V. R. Prasad, “N-person differential games and multicriterion optimal control problems,” Ph. D. Thesis, Department of Electrical Engineering, Indian Institute of Technology, Kaneur (1969).
V. R. Prasad and I. G. Sarma, “Theory of N-person differential games,” Proc. 1st Int. Conf. Theory and Applic. Different. Games, Amherst, Mass., 1969, S.1., s.a., viii/12–viii/17.
V. R. Prasad and I. G. Sarma, “Stochastic multicriterion optimal control problems,” Proc. IEEE Symp. Adap. Processes (9th) Decis. and Contr., Austin, Texas, 1970. New York (1970), XV15/1–XV15/5.
G. Pravin, “N-player stochastic differential games,” SIAM J. Control, Optimiz.,14, No. 3, 538–545 (1976).
Z. V. Rekasius and W. E. Schmitendorf, “On the noninferiority of Nash equilibrium solutions,” IEEE Trans. Autom. Control,16, No. 2, 170–173 (1971).
Z. V. Rekasius and W. E. Schmitendorf, “Comments on On the noninferiority of Nash equilibrium solutions,” IEEE Trans. Autom. Control, AC-17 (1972).
H. Rommelfanger, “Ein Verfahren zur Lösung Dynamischer N-Personensuperspiele,” Proc. Operat. Res., Wurzburg-Wien, 181–189 (1973).
A. P. Sage, “On gradient methods for optimization of differential game strategies,” SWIEEE Co Rec. Techn. Pap. 22nd Annu. Southwest, IEEE Conf. and Exhibit., Dallas, Texas, 1970, New York, 1970, pp. 188–191.
M. Sakawa, “An approximate solution of linear multicriteria control problems through the multicriteria simplex method,” J. Optimiz. Theory Appl.,22, No. 3, 417–427 (1977).
M. Sakawa and Y. Sawaragi, “Multiple-objective optimization for environment development systems,” Int. J. Syst. Sci.,6, No. 2, 157–164 (1975).
M. Sakawa and Y. Sawaragi, “Multiple-criteria optimization of pollution control model,” Int. J. Syst. Sci.,6, No. 8, 741–748 (1975).
M. Sakawa and Y. Sawaragi, “Multiple-criteria optimization for environment development system —constrained case,” Mem. Fac.Eng. Kyoto Univ.,37, No. 3, 176–183 (1975).
M. Sakawa and Yoshikatsu Ueda, “The optimal control of environmental pollution and economic growth,” Trans. Soc. Instrum. Control Eng.,13, No. 2, 194–199 (1977).
A. I. Salama, “Optimization of systems with several cost functionals,” Ph. D. Dissertation, Dept. of Electr. Eng., Univ. of Alberta, Edmonton, Canada (1970).
A. I. Salama and V. Gourishankar, “Optimization of a deterministic system with two control functions and several cost functionals,” Proc. 4th Haw. Int. Conf. Syst. Sci., Honolulu, Haw., 1971, North Hollywood, Calif., 1971, pp. 371–373.
A. I. Salama and V. Gourishankar, “Optimal control of systems with a single control and several cost functionals,” Int. J. Control,14, No. 4, 705–725 (1971).
M. E. Salukvadze, “On optimization of control systems according to vector-valued performance criteria,” Proc. IFAC 5th World Contr., 1972, Part 4, S.1., s.a., 40-5/1–40-5/7.
M. E. Salukvadze, “On the existence of solutions in problems of optimization under vector-valued criteria,” J. Optimiz. Theory Appl.,13, No. 2, 203–207 (1974).
I. G. Sarma, U. R. Prasad, and R. K. Ragade, “Necessary conditions for optimal strategies in a class of noncooperative N-person differential games,” SIAM J. Contr.,7, No. 4, 637–644 (1969).
I. G. Sarma and R. K. Ragade, “Some considerations in formulating optimal control problems as a differential games,” Int. J. Control,4, No. 3, 264–279 (1966).
M. A. Save, “A general criterion for optimal structural design,” J. Optimiz. Theory Appl.,15, No. 1, 119–129 (1975).
W. E. Schmitendorf and G. Leitmann, “A simple derivation of necessary conditions for Pareto optimality,” IEEE Trans. Autom. Control,19, No. 5, 601–602 (1974).
W. E. Schmitendorf and J. A. Walker, “On the equivalence of some necessary conditions for vector-valued criteria problems,” IEEE Trans. Autom. Control,18, No. 6, 664–665 (1973).
W. E. Schmitendorf, “Cooperative games and vector-valued criteria problems,” Proc. IEEE Conf. Decis. and Control and 11th Symp. Adapt. Proc., New Orleans, La., 1972, New York, 1972, pp. 340–344.
Naresh K. Sinha, “Reduction of the sensitivity of optimal control systems by using two degrees of freedom,” Sensitivity Adaptivity and Optimality. Proc. 3rd IFAC Symp. Ischia, 1973. Pittsburgh, Pa., 1973, pp. 267–270.
K. Spremann, “Über Vektormaximierung und Analyse der Gewichtung von Subzielen,” in: Lect. Notes Econ. Math. Syst.,117 (1976), pp. 283–296.
W. Stadler, “Sufficient conditions for preference optimality,” in: Multicriter. Decision Mak. and Differential Games, New York-London (1976), pp. 129–148.
H. L. Stalford, “Criteria for Paretooptimality in cooperative differential games,” J. Optimiz. Theory Appl.,9, No. 6, 391–398 (1972).
H. L. Stalford, “Sufficient conditions for optimal control with state and control constraints,” J. Optimiz. Theory Appl.,7, No. 2, 118–135 (1971).
A. W. Starr, “Nonzero-sum differential games. Concepts and models,” Harvard University, Division of Engineering and Applied Physics, Technical Report, No. 590, May, 1969.
A. W. Starr and Y. C. Ho, “Nonzero-sum differential games,” J. Optimiz. Theory Appl.,3, No. 3, 184–204 (1969).
A. W. Starr and Y. C. Ho, “Further properties of nonzero-sum differential games,” J. Optimiz. Theory Appl.,3, No. 4, 207–219 (1969).
R. I. Stern and Adi Ben-Israel, “An inferior penalty function method for the construction of efficient point in a multicriteria control problem,” J. Math. Anal. Appl.,46, No. 3, 768–776 (1974).
C. S. Tapiero and J. V. Farley, “Optimal control of sales force effort in time,” Manage. Sci.,21, No. 9, 976–985 (1975).
R. M. Thrall, “Game theory and some interfaces with control theory,” Lect. Notes Econ. Math. Syst.,105, 310–391 (1974).
P. Varaiya, “N-player stochastic differential games,” SIAM J. Control Optimiz.,14, No. 3, 538–545 (1976).
P. Varaiya, “N-person stochastic differential games,” in: Theory and Appl. Differ. Games, Dordrecht-Boston (1975), pp. 97–107.
Z. Varga, “Least-squares solution for N-person multicriteria differential games,” Ann. Univ. Sci., Budapest. Sec. Math.,21, 139–148 (1978).
V. V. Velichenko, “Sufficient conditions for absolute minimum of the maximal functional in the multicriterial problem of optimal control,” Lect. Notes Comput. Sci.,27, 220–225 (1975).
T. L. Vincent and G. Leitmann, “Control-space properties of cooperative games,” J. Optimiz. Theory Appl.,6, No. 2, 91–113 (1970).
F. M. Walts, “An engineering approach to hierarchical optimization criteria,” IEEE Trans. Autom. Control,AC-12, No. 2, 179–180 (1967).
Y. H. Wan, “On local Paretooptima,” J. Math. Econ.,2, No. 1, 35–42 (1975).
E. R. Weintraub and M. G. Myers, “A dynamic model of firm entry,” Rev. Econ. Stud.,38, No. 1, 127–129 (1971).
R. E. Wendell and D. N. Lee, “Efficiency in multiple objective optimization problems,” Math. Program., No. 12, 406–414 (1977).
P. L. Yu, “A class of solutions for group decision problems,” Center for System Science, 71-06, Graduate School of Management, Univ. of Rochester, New York (1972).
P. L. Yu, “Introduction to domination structures in multicriteria decision problems.” System Analysis Program., Working Paper Series No. F-7219, Graduate School of Management, Univ. of Rochester, New York (1972).
P. L. Yu, “Nondominated investment policies in stock markets (including an empirical study),” System Analysis Program., Working Paper Series No. F-7222, Graduate School of Management, University of Rochester, New York (1972).
P. L. Yu, “Cone convexity, cone extreme points and nondominated solution in decision problems with multiobjectives,” Center for System Science 72-02, Graduate School of Management, University of Rochester, New York (1972).
P. L. Yu, “Cone convexity, cone extreme points and nondominated solution in decision problems with multiobjectives,” J. Optimiz. Theory Appl.,14, No. 3, 319–377 (1974).
P. L. Yu, “A class of solutions for group decision problems,” Manage. Sci.,19, No. 8, 936–946 (1973).
P. L. Yu and G. Leitmann, “Confidence structures in decision making,” IFAC Symp. on Large Scale Systems, Udine, 1976.
P. L. Yu and G. Leitmann, “Nondominated decisions and cone convexity in dynamic multicriteria decision problems,” J. Optimiz. Theory Appl.,14, No. 5, 573–584 (1974).
P. L. Yu and G. Leitmann, “Compromise solutions, domination structures and Salukvadze's solution,” J. Optimiz. Theory Appl.,18, No. 4, 119–140 (1976).
L. A. Zadeh, “Optimality and nonscalar-valued performance criteria,” IEEE Trans. Autom. Control.,AC-8, No. 1, 59–60 (1963).
M. Zeleng, MCDM Bibliography, 1975, Lect. Notes Econ. Math. Syst.,123, 291–321 (1976).
A. Zieba, “An example of pursuit theory,” Stud. Math.,22, No. 1, 1–6 (1962).
Additional information
Translated from Itogi Nauki i Tekhniki, Matematicheskii Analiz, Vol. 17, pp. 3–112, 1979.
The authors thank V. V. Al'sevich, É. M. Vaishbord, Z. Varga, V. V. Velichenko, V. V. Gorokhovik, V. I. Zabotin, A. F. Kanonenko, V. B. Kolmanovskii, I. A. Kornienko, O. A. Malafeev, V. S. Molostvov, V. V. Morozov, V. V. Podinovskii, V. E. Ryzhova, M. E. Salukvadze, S. V. Chistyakov for comments, many of which were taken into account in the final formulation of the manuscript.
Rights and permissions
About this article
Cite this article
Tynyanskii, N.T., Zhukovskii, V.I. Differential games with nonzero sum (cooperative variant). J Math Sci 15, 369–438 (1981). https://doi.org/10.1007/BF01375562
Issue Date:
DOI: https://doi.org/10.1007/BF01375562