A video game apparatus is provided, and can function either as a stand alone single entity game or as a peer game communicating in a single identity game system. The function of each video game apparatus can then be defined at the start of game play. Alternatively, each of the video game apparatus can be limited in function to a peer game in the system. The video game apparatus has a user input device and an associated video display. The user selects a distinguishable visual image representation by which that user is identified. For example, color, size or shape can be used to distinguish users. In one embodiment a digitized image of each user's face is used as the distinguishable representation. Alternatively, the user can create an original image or select one of a predetermined set of visual images as the user's identification for use in the video game audiovisual presentation. Where multiple users are playing a single identity (global) game, each user can select a unique but personal visual representation identify for use in the video game audiovisual presentation.