A technology of realizing wireless communication between a parent station and child stations with efficiency. In a game system according to the present invention, a game apparatus sets the maximum number of times of transmission for wireless game controllers, in accordance with the number of wireless game controllers that are communicating at a predetermined communication cycle. Here, time for establishing connection with a new wireless game controller is reserved within each communication cycle, thereby allowing new users to join the game. The maximum number of times of transmission is re-set when the number of wireless game controllers connected changes.