Geodesic
Cooperative differential game model with continuous updating
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 2, pp. 82-109.

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The paper considers and describes the class of cooperative differential games with continuous updating. Such a class of differential games is new, at the moment only the class noncooperative game models with continuous updating have been studied. This paper describes the process of constructing cooperative strategies, cooperative trajectory, characteristic function and cooperative solution with continuous updating. Cooperative case of limited resource extraction game model with continuous updating is considered. Optimal strategies, characteristic function and cooperative solution are constructed. The Shapley vector is used as a cooperative solution. The numerical simulation results are demonstrated in the Matlab environment.
Keywords: differential games, continuous updating. 
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Ovanes L. Petrosian; Anna V. Tur; Zeyang Wang; Hongwei Gao. Cooperative differential game model with continuous updating. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 2, pp. 82-109. http://geodesic.mathdoc.fr/item/MGTA_2020_12_2_a4/

[1] Basar T., Olsder G. J., Dynamic noncooperative game theory, Academic Press, London, 1995 | MR | Zbl

[2] Bellman R., Dynamic Programming, Princeton University Press, Princeton, 1957 | MR | Zbl

[3] Bercovitz L., “A variational approach to differential games”, Adv. in game theory, Ann. of Math. Studies, 1964, 127–175 | MR

[4] Chistyakov S., “On non-cooperative differential games”, Reports of the USSR Academy of Sciences, 259:5 (1981), 1052–1055 | MR

[5] Dockner E., Jorgensen S., Long N., Sorger G., Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, 2000 | MR | Zbl

[6] Fleming W., “The convergence problem for differential games”, Adv. in game theory, Ann. of Math. Studies, 1964, 175–195 | MR

[7] Gromova E., Petrosian O., “Control of informational horizon for cooperative differential game of pollution control”, International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2016, 1–4

[8] Gromova E. V., Petrosyan L. A., “Strongly dynamically stable cooperative solution in one differential game of harmful emissions management”, Managing large systems, 55 (2015), 140–159

[9] Haurie A., “A note on nonzero-sum differential games with bargaining solutions”, Journal of Optimization Theory and Applications, 18:1 (1976), 31–39 | DOI | MR | Zbl

[10] Kleimenov A., Non-antagonistic positional differential games, Science, Ekaterinburg, 1993 | MR

[11] Kononenko A., “On equilibrium positional strategies in non-antagonistic differential games”, Reports of the USSR Academy of Sciences, 231:2 (1976), 285–288 | MR | Zbl

[12] Krasovsky N., Control of Dynamical System. Problem of minimum guaranteed result, Science, Moscow, 1985 | MR

[13] Kuchkarov I., Petrosian O., On class of linear quadratic non-cooperative differential games with continuous updating, Lecture Notes in Computer Science, 11548, 2019 | Zbl

[14] Petrosian O., Gromova E., “Cooperative differential games with dynamic updating”, IFAC-PapersOnLine, 51:32 (2018), 413–417 | DOI

[15] Petrosian O. L., Nastych M. A., Volf D. A., Non-cooperative differential game model of oil market with looking forward approach, Frontiers of Dynamic Games, Game Theory and Management, Birkhauser, Basel, 2018 | DOI | MR | Zbl

[16] Petrosian O. L., Nastych M. A., Volf D. A., “Differential game of oil market with moving informational horizon and non-transferable utility”, 2017 Constructive Nonsmooth Analysis and Related Topics, dedicated to the memory of V. F. Demyanov, 2017

[17] Petrosian O., “Looking forward approach in cooperative differential games”, International Game Theory Review, 18:2 (2016), 1–14 | MR

[18] Petrosian O., “Looking forward approach in cooperative differential games with infinite-horizon”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2016, no. 4, 18–30 | MR

[19] Petrosian O., Barabanov A., “Looking forward approach in cooperative differential games with uncertain-stochastic dynamics”, Journal of Optimization Theory and Applications, 172:1 (2017), 328–347 | DOI | MR | Zbl

[20] Petrosian O., Tur A., “Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating”, Communications in Computer and Information Science, 1090 (2019), 178–191 | DOI | MR

[21] Petrosyan L. A., Danilov N. N., “Time consistency of solutions for non-antagonistic differential games with transferable payoffs”, Vestnik of Leningrad University. Ser. 1: Mathematics, Mechanics, Astronomy, 1 (1979), 52–59 | MR | Zbl

[22] Petrosyan L. A., Danilov N. N., Cooperative differential games and their applications, Publishing house of Tomsk University, 1985 | MR

[23] Petrosyan L., “Time consistency of solutions for differential games with many participants”, Vestnik of Leningrad University. Ser. 1: Mathematics, Mechanics, Astronomy, 1977, no. 4, 46–52 | Zbl

[24] Petrosyan, L., “Strong time consistent differential optimality principles”, Vestnik of Leningrad University. Ser. 1: Mathematics, Mechanics, Astronomy, 1993, no. 4, 35–40 | MR | Zbl

[25] Petrosyan L. A., Murzov N. V., “Game-theoretic problems in mechanics”, Lithuanian Mathematical Collection, 1966, no. 3, 423–433 | MR

[26] Petrosyan L. A., Tomsky G.V, Dynamic games and their applications, Leningrad State University, Leningrad, 1982 | MR

[27] Petrosyan L. A., Zaccour G., “Time-consistent Shapley value allocation of pollution cost reduction”, J. Econ. Dyn. Control, 27:3 (2003), 381–398 | DOI | MR

[28] Pontryagin L., “On theory of differential games”, Successes of Mathematical Sciences, 26:4(130) (1966), 219–274 | MR

[29] Shapley L., “A value for n-person games”, Contributions to the Theory of Games II, Annals of Mathematics Studies, 28, eds. H. W. Kuhn, A. W.Tucker, 1953, 307–317 | MR | Zbl

[30] Shevkoplyas E., “Optimal solutions in differential games with random duration”, Journal of Mathematical Sciences, 199:6 (2014), 715–722 | DOI | MR | Zbl

[31] Shi L., Petrosian O., “A dynamic oligopoly marketing model of advertising”, Contributions to Game Theory and Management, 11 (2018), 207–223 | MR

[32] Tolwinski B., Haurie A., Leitmann G., “Cooperative equilibria in differential games”, Journal of Mathematical Analysis and Applications, 119:1 (1986), 182–202 | DOI | MR | Zbl

[33] Yeung D., Petrosian O., “Cooperative stochastic differential games with information adaptation”, International Conference on Communication and Electronic Information Engineering (CEIE 2016), 2017, 1–13

[34] Zaccour G., “Time consistency in cooperative differential games: A tutorial”, INFOR: Information Systems and Operational Research, 46:1 (2008), 81–92 | MR