There is provided a game system which makes it possible to implement a transaction desired by a side which receives a game element. When delivering a game element from a user of a first game machine 1 to a user of a second game machine 1, transaction information for identifying game elements possessed by the user of the first game machine is provided to the second machine. In the second game machine, a list of acquirable game elements is displayed according to the provided transaction information. The user of the second game machine is urged to select a game element to be acquired, from the displayed game elements. The selection result is returned from the second game machine to the first game machine. In the first game machine, data identifying the possession state of game elements is updated so as to decrease the game element deprived of from the possession range of the user. In the second game machine, data identifying the possession state of game elements is updated so as to add the acquired game element to the possession range of the user.