Geodesic
Information solvability in multistage games with a~set of players of arbitrary cardinality
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 3 (2011) no. 4, pp. 99-127.

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Multistage games with separated dynamics, with a set of players of arbitrary cardinality are investigated in the paper. To describe the information structure of a game a concept of information vector-function of a player determined by the author in the previous work is used. It is shown that the condition of information solvability for the games with finite set of players introduced earlier is insufficient for the class of games involved. The definition of information solvability of an ordered according to players set of information vector-functions for the games with infinite set of players is introduced. It is noted that this definition and the one introduced by the author in the previous work for multistage games with finite set of players are equivalent. The axiomatics of multistage games with separated dynamics is given.
Keywords: multistage game with a set of players of arbitrary cardinality, information vector-function, information solvability, axiomatics of multistage games. 
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Nikolai M. Slobozhanin. Information solvability in multistage games with a~set of players of arbitrary cardinality. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 3 (2011) no. 4, pp. 99-127. http://geodesic.mathdoc.fr/item/MGTA_2011_3_4_a4/

[1] Petrosyan L. A., Tomskii G. V., Differentsialnye igry s nepolnoi informatsiei, Izd-vo IrGU, Irkutsk, 1984 | MR | Zbl

[2] Slobozhanin N. M., Informatsiya i upravlenie v dinamicheskikh igrakh, Izdatelstvo SPbGU, Sankt-Peterburg, 2002

[3] Slobozhanin N. M., “Informatsionnaya razreshimost v mnogoshagovykh igrakh s konechnym mnozhestvom igrokov”, Matematicheskaya teoriya igr i ee prilozheniya, 3:2 (2011), 81–101 | MR | Zbl

[4] Kuhn H., “Extensive games and the problem of information”, Contributions to the theory of games, v. 2, Annals of Mathematics Studies, 28, 1953, 193–216 | MR | Zbl

[5] Scarf H., Shapley L., “Game with partial information”, Contributions to the theory of games, v. 3, Annals of Mathematics Studies, 39, 1957, 213–229 | MR