For mathematical formalization of differential positional game

V. I. Zhukovskii^a, L. V. Zhukovskaya^b, L. V. Smirnova<sup>c

a</sup> Moscow State University named after Lomonosov, Faculty of Computational Mathematics and Cybernetics, Department of Optimal Control, Leninskiye Gory, GSP-1, Moscow, 119991, Russia
^b Federal State Budgetary Institution of Science Central Economic and Mathematical Institute of the Russian Academy of Sciences (CEMI RAS), Nakhimovskii prosp., 47, Moscow, 117418, Russia
^c State University of Humanities and Technology, Zelenaya, 22, Orekhovo-Zuevo, 142611, Russia

Abstract: The academician Andrey Izmailovich Subbotin proposed in 1988 the counterexample for used in that time mathematical formalization of positional differential game: it turned out that during the time of duration of the game new motions can appear which could not be taken into account in initial position. Namely the present article is devoted to these problems.

Keywords: differential game, noncooperative game, step-by-step motion, quasimotion, terminal payoff functions.

UDC: 517.977.8

MSC: 91A23

Language: English