A game system includes a plurality of game apparatuses that can carry out short-range wireless communication with one another. Link strength is detected for wireless communication between a parent apparatus and a child apparatus selected as a communication partner thereof. If the link strength is not equal to or more than a predetermined value, the image of a rare item piece is not displayed and the image of a normal item piece alone is displayed even though the partner has the rare item pieces in its possession, for example. Also, the use of the rare item is not permitted. On the other hand, if the link strength is equal to or more than the predetermined value, the use of the rare item is permitted and, if the combination of rare item pieces is successful, for example, the rare item is used.