ABOUT GAMES LIKE THE BANACH-MAZUR GAME

UDC 517.5
DOI: 10.36871/2618-9976.2022.10.001

Authors

Evgeny V. Manokhin
Candidate of Physical and Mathematical Sciences, Associate Professor, Head of the Department of Mathematics and Computer Science, Tula filial of Financial university, Tula, Russia
Irina V. Dobrynina
Doctor of Physical and Mathematical Sciences, Associate Professor, Professor of the Department of Higher Mathematics, Academy of Civil Protection EMERCOM of Russia, Khimki, Russia
Nadezhda О. Kozlova
Candidate of Technical Sciences, Senior Lecturer of the Department of Mathematics and Computer Science, Tula filial of Financial university, Tula, Russia

Abstract

This article introduces a new class of games, which we will call G-games. One of the representatives of this class is the famous Banach–Mazur game. Some properties of convexity and smoothness of Banach spaces in connection with G-games are analyzed. An overview of mainly dynamic games developed by a number of authors in recent years is presented, the application of which can be expanded beyond the scope of the situations under consideration and used to analyze other processes.

Keywords

Game theory, Banach space, Normed space, Locally uniform convexity of Banach space