Geodesic
New characteristic function for multistage dynamic games
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 4, pp. 316-324 Cet article a éte moissonné depuis la source Math-Net.Ru

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The finite stage dynamic $n$-person games with transferable payoffs are considered. The cooperative version of the game is defined, and a new approach for constructing characteristic functions in multistage games based on characteristic functions defined in stage games is proposed. It is proved that the values of this new characteristic function dominate the values of characteristic function constructed using the min-max approach. This allows constructing the subcore of the classical core in the multistage game under consideration and guarantees that this new approach leads to time-consistent (works L. Petrosyan, G. Zaccour, 2003; L. Petrosyan, 1991) and in some cases strongly time-consistent solutions (paper L. Petrosyan, 1993). The example is provided showing the construction of this newly defined characteristic function and the time-consistency and strong time-consistency of the core.
Keywords: multistage game, characteristic function, time-consistency, strongly time-consistency. 
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     title = {New characteristic function for multistage dynamic games},
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Y. B. Pankratova; L. A. Petrosyan. New characteristic function for multistage dynamic games. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 4, pp. 316-324. http://geodesic.mathdoc.fr/item/VSPUI_2018_14_4_a3/

[1] Von Neumann J., Morgenstern O., Theory of games and economic behavior, Princeton University Press, Princeton, 1953, 666 pp. | MR | Zbl

[2] Basar T., “Time consistency and robustness of equilibria in noncooperative dynamic games”, Dynamic Policy Games in Economics, eds. F. Van der Ploeg, A. de Zeew, North-Holland, Elsevier Science Publ., Amsterdam, 1989, 9–54 | MR

[3] Beard R., McDonald S., “Time consistent fair water sharing agreements”, Ann. Intern. Soc. Dyn. Games, 9, Birkhauser Publ., Boston, 2007, 393–410 | DOI | MR | Zbl

[4] Marin-Solano J., “Time-consistent equilibria in a differential game model with time inconsistent preferences and partial cooperation”, Dynamic Games in Economics, Springer Publ., Berlin, 2014, 219–238 | DOI | MR | Zbl

[5] Yeung D. W. K., Petrosyan L. A., Cooperative stochastic differential games, Springer-Verlag Publ., New York, 2006, 253 pp. | MR | Zbl

[6] Petrosyan L. A., “Strongly time-consistent differential optimality principles”, Vestnik of Saint Petersburg University. Series Matematics. Mechanics. Astronomy, 1993, no. 4, 35–40 | MR | Zbl

[7] Petrosyan L. A., Gromova E. V., “On an approach to constructing a characteristic function in cooperative differential games”, Automation and Remote Control, 78:9 (2017), 1680–1692 | DOI | MR

[8] Petrosyan L., Zaccour G., “Time-consistent Shapley value allocation of pollution cost reduction”, Journal of Economic Dynamics and Control, 27:3 (2003), 381–398 | DOI | MR

[9] Petrosyan L. A., “Time consistency of the optimality principles in non-zero sum differential games”, Lecture Notes in Control and Information Sciences, 157, 1991, 299–311 | DOI | MR