There are several distinct types of Multiplayer modes in Video Games. This trope is a Sister Trope of Meta Multiplayer, Co-Op Multiplayer and Massively Multiplayer.
See also Misbegotten Multiplayer Mode, where multiplayer modes are featured in games that are really designed for single-player.
Competitive
Players directly compete against each other (Player Versus Player) and possibly characters [...] [tvtropes.org]