A multi-player game system (100) includes a lobby server (3) and a plurality of game devices (A1, A2, . . . and B1, B2, . . . ). When there is a preceding entry game device in a competition waiting state, since the server device has already received an entry request from the preceding entry game device, the lobby server (3) indicates the preceding entry game device as an opponent to a new entry game upon receiving an entry list request from the new entry game device. This indication is issued irrespective of the round of the knockout competition in which each of the new entry game device and the preceding entry game device is. The game device manages the round of the knockout competition in which the game device is, progresses the game device to the next round on the basis of determination as to whether or not the game device has won, and causes a display of the game device to show an image corresponding to the round.