A competitive game program and virtual game player list are previously stored in a server. The server provides on network a competitive game service to a plurality of game players' terminals via communication lines. The server sets such that, under the condition that the number of competitors against the game players is below a predetermined number, the competitive game program is activated to play the competitive game with the game players, and notifies, as a competitor, a virtual game player's name previously entered on the virtual game player list, to the game players who are to play the competitive game with the competitive game program. Therefore, the game player can enjoy the competitive game with the virtual game player, even if the number of competitors is insufficient when receiving the competitive game service. This avoids the inconvenience that although the game player (user) has access to the competitive game site for the purpose of playing the competitive game, the player cannot help giving up playing the game.