Tournament
The game mode named Tournament is offered by various shooter type games, such as Toxikk or Star Trek: Voyager Elite Force. It is very similar to the deathmatch mode but the number of players is limited to two, fighting each other. Usually the normal Deathmatch rules are applied, meaning a match ends when either a designated number of frags was reached by a player or a time limit was hit. Other than normally, the server will keep track of the results of the matches for both players, giving them a score a little more rough than the normal match scores.
As an example: First player A wins, then player B wins, then player A wins again. Then the score is 2:1 for player A, regardless of the details of the single matches frag counts. This style is used by Star Trek: Voyager Elite Force.
Another variation is when more players are allowed to be active on the same server, the duel combinations are rotated. Whenever a player gets fragged, he is moved to spectator and another takes his place. So each player will have to play against any other player at some point but always 1 on 1. All other players not currently actively participating in combat are spectators. The one with the highest frag count wins. This style is used by Toxikk.