The invention relates to a computer system for playing a competing type computer game. Specific characteristic data of each of game players is stored in a memory card for each game player. The specific characteristic data is movable from one memory to another memory in accordance with result of the competing game. The memory card is detachable from the computer system. Further, the computer system is able to be connected with a network. Therefore, the skill of the game player is displayed and stored clearly and correctly. Further, the skills of each of the game players is displayed on all display units of the game players on the network at the same time. Therefore, all game players are able to play the same computer game at the same time on the network and any game player is able to recognize the skills of any other game players on the network.