It sounds like arcade Soul Calibur 2's Conquest mode, to me.
For those unfamiliar, Conquest mode was an arcade-only affair with a persistent contest of 4 factions. When you start, you pick your character, your name, password, and 1 of the 4 factions. One playthrough is against eight AI opponents. 1 round each. Some of these AIs are computer-generated, some are actual AI ghosts of other players on that arcade machine. As you keep winning, your character levels up, which makes its ghost AI much harder, and your faction gains more territory on the world map. One person could have multiple characters on the same machine if they wanted. After a set amount of time, the territories would reset, but the characters and their levels would remain, and it started over again.
The thing that sucked about Conquest was that there was never any direct competition. The top player in blue faction could never fight the top player in red faction for territory in an actual fight; only player vs AI fights counted. The thing that was good about Conquest, though, is that casuals played it like nobody's business. I'd see people play multiple times in one sitting just because they were that hooked on leveling up their fighter and trying to get their faction the lead. It made arcade SCII ridiculously popular, and even got a few of the casuals to actually learn and play the game against real competition rather than just grinding AI.
I always said that Conquest mode would've been cool as hell if the mode was focused on actual direct competition between factions instead of dumb AI battles. Now, 10 years later, I hear Boon talking about a persistent online contest....
