Geodesic
Cooperative optimality principals in differential games on networks
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 4, pp. 93-111.

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The paper describes a class of differential games on networks. The construction of cooperative optimality principles using a special type of characteristic function that takes into account the network structure of the game is investigated. The core, the Shapley value and the $\tau$-value are used as cooperative optimality principles. The results are demonstrated on a model of a differential research investment game, where the Shapley value and the $\tau$-value are explicitly constructed.
Keywords: differential games, games on networks, cooperative game. 
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Anna V. Tur; Leon A. Petrosyan. Cooperative optimality principals in differential games on networks. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 4, pp. 93-111. http://geodesic.mathdoc.fr/item/MGTA_2020_12_4_a5/

[1] D. A. Novikov, “Igry i seti”, Matematicheskaya teoriya igr i ee prilozheniya, 2:1 (2010), 107–124 | MR | Zbl

[2] A. Sedakov, Dinamicheskie setevye igry, dis. ... d-ra fiz. mat. nauk, Sankt-Peterburgskii. gos. universitet, SPb., 2020

[3] L. A. Petrosyan, “Kooperativnye differentsialnye igry na setyakh”, Tr. IMM UrO RAN, 16, no. 5, 2010, 143–150

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

[5] H. Gao, Ya. Pankratova, “Cooperation in Dynamic Network Games”, Contributions to Game Theory and Management, 10 (2017), 42–67 | MR

[6] D. B. Gillies, “Solutions to general non-zero-sum games”, Contributions to the Theory of Games IV, Annals of Mathematics Studies, 40, eds. Tucker A.W., Luce R.D., Princeton University Press, Princeton, 1959, 47–85 | MR

[7] E. Gromova, E. Marova, D. Gromov, “A substitute for the classical Neumann-Morgenstern characteristic function in cooperative differential games”, Journal of Dynamics Games, 7:2 (2020), 105–122 | DOI | MR | Zbl

[8] Gromova E.V., Petrosyan L.A., “On an approach to constructing a characteristic function in cooperative differential games”, Autom. Remote Control, 78 (2017), 98–118 | DOI | MR | Zbl

[9] M. O. Jackson, Y. Zenou, Games on Networks, Handbook of Game Theory, 4, eds. Peyton Young, Shmuel Zamir, Elsevier Science, 2014 | MR

[10] V. Mazalov, J. V. Chirkova, Networking Games: Network Forming Games and Games on Networks, Academic Press, 2019 | Zbl

[11] L. Petrosyan, D. Yeung, “Shapley value for differential network games: Theory and application”, Journal of Dynamics Games | DOI | MR

[12] L. Petrosyan, D. Yeung, “Construction of Dynamically Stable Solutions in Differential Network Games”, Stability, Control, Differential Games, Lecture Notes in Control and Information Sciences, eds. Tarasyev A., Maksimov V., Filippova T., Springer, Cham, 2020 | MR | Zbl

[13] L. S. Shapley, “A value for n-person games”, Contributions to the Theory of Games, v. 2, Annals of Mathematics Studies, 28, Princeton University Press, Princeton, NJ, 1953 | MR

[14] S. Tijs, “Bounds for the core of a game and the t-value”, Game Theory, Mathematical Economics, eds. Moeschlin O., Pallaschke D., North-Holland Publishing Company, Amsterdam, 1981, 123–132 | MR

[15] S. Tijs, “An axiomatization of the t-value”, Mathematical Social Sciences, 13:2 (1987), 177–181 | DOI | MR | Zbl

[16] J. Von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1953 | MR | Zbl