Some remarks on games of certain star selection principles

We present game-theoretic observations related to certain star selection principles initiated in Kocinac [8]. We mainly focus on the variations of games related to Menger, Hurewicz and Rothberger properties. We correlate the games associated to star selection principles with the games corresponding to the classical selection principles under certain topological assumptions. Few examples are illustrated to show that the games related to the star selection principles and the classical ones are not equivalent. We also define restricted star-Menger game and investigate its relationship with the restricted Menger and few other related games. The relationship between winning strategies of the players in the games considered here are summarized into an implication diagram.