About Games Like the Banach-Mazur Game

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.