I am perfectly aware of to what you were commenting on. I am saying you are wrong. They did fight people of varying origins and exotic animals (including tigers... actually, when people fought animals they weren't called gladiators, they were called bestiarius) from all around the Roman Empire. They also went beyond one on one combat, they recreated battles on land and on sea. Some of the events that actually happened in the Coliseum (and other ampitheatres) were more outlandish than anything Hollywood would dare put on screen. As for chariots, there were chariots involved in Coliseum battles and some minor races but most of the better chariot races happened at the Circus Maximus.
Edit: If you are interested in learning more about Gladiators and other battles at the Coliseum, I highly recommend reading, Liber Spectaculorum or The Book of Spectacle by M. Valerii Martialis.
Both of you are right.
Gladiators (with only few exceptions) just fought one on ones. Sometimes there where 10 or more pairs of gladiators fighting at the same time with very strict rules (as werekitten said with special type of gladiators fighting each other).
The large combats where a speciality within the time of the emperors and didn't involve gladiators, but war prisoners. The bestiarii where mainly convicted non-Romans. Martials "liber spectaculorum" is still disputed in science, because historians can't simply figure out, how they actually flood the colosseum, but the mass land combats have been proven as a historical fact.