Game apparatuses connected in a peer-to-peer manner play a competitive game with each other. Each of the game apparatuses stores a ranking table ranking points of multiple users based on past games of the users. When finishing playing the game, the game apparatuses respectively calculate points obtained by the respective users based on the result of the game, and update the ranking tables based on the newly calculated points. The game apparatuses transmit and receive information on the updated ranking table to and from each other. Each game apparatus integrates the ranking table locally stored with the ranking table transmitted from the other game apparatus to generate a new ranking table, and displays the new ranking table on a display device.