Can PlayStation 3 games be played on a PlayStation 2?

No it is a PS3 and the PS3 games can not play on a PS2. Only one of the reason is that the PS2 can not read Bluray discs. Another is that it does not have the hardware for the game to work. There is a reason the PS3 costs more than a PS2 even now almost 5 years after it's release and the PS2 will never play PS3 games