A turn-based combat system where characters move in order of initiative (or related stat, such as speed) regardless of their side in the conflict.
Alternate names: Turns by initiative, Unit initiative
The first video game about Initiative was released in 1994.
Called Time Count System or some such in FFX.
This is an attempt to bring more realism (and more tactics) to turn-based games where "faster" units get to act before "slower" units, as movement is no longer bound to each player having a turn on which they move single unit or all units they have.