Dogfight is an aerial combat video game released for the Apple II computer in 1980. A later version, Dogfight II, is copyrighted 1983. It is essentially a shoot 'em up style game, with the player controlling an aircraft which they can steer in one axis (left or right) and shoot. Similar to Asteroids, the screen wraps around at the edges, such that a player heading off the right edge of the screen will re-enter from the left.
Players can play solo against the computer, or, in a system very unusual in video games, up to 8 humans can play against each other. Since all control is via the single built-in keyboard of the Apple II, this involves the players crowding up against each other to reach their 3 keys. Each plane is identified by a number drawn next to it.
When a plane is shot, it becomes a parachuting figure, which transits the screen from top to bottom a few times and also may be shot.
Source: Wikipedia, "Dogfight (1980 video game)", available under the CC-BY-SA License.