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Wiktionary
player versus player

n. (context video games chiefly role-playing games English) A form of multiplayer interaction in which human players compete against each other, rather than cooperate or battling computer-controlled opponents.

Wikipedia
Player versus player

Player(s) versus player(s), or PvP, is a type of multiplayer interactive conflict within a game between two or more live participants. This is in contrast to games where players compete against computer-controlled opponents and/or players, which is referred to as player versus environment (PvE). The terms are most often used in games where both activities exist, particularly MMORPGs, MUDs, and other role-playing video games. PvP is sometimes called player killing or PKing..

PvP can be broadly used to describe any game, or aspect of a game, where players compete against each other.

PvP is often controversial when used in role-playing games. In most cases, there are vast differences in abilities between experienced and novice players. PvP, when poorly designed, can encourage experienced players to immediately attack and kill inexperienced players before they have even had an opportunity to play.