God of War Games on PS3: Which Ones Are Playable?

"War 2" doesn't exist. You're thinking of the God of War franchise. Here's the PS3 lineup:

Game	Original Platform	On PS3?
God of War (2005)	PS2	No (PS2 only; playable on PS3 via software BC on launch 60GB/20GB models only)
God of War II (2007)	PS2	No (same as above)
God of War Collection (2009)	PS3	Yes — Remastered GoW 1 & 2 at 720p/60fps, trophies.
God of War III (2010)	PS3	Yes — Native PS3 exclusive.
God of War: Origins Collection (2011)	PS3	Yes — Remastered Chains of Olympus & Ghost of Sparta (PSP games).
God of War: Ascension (2013)	PS3	Yes — Native PS3, prequel, multiplayer.
God of War (2018)	PS4	No (PS4/PC only).
God of War Ragnarök	PS4/PS5	No.

PS5: God of War Collection (PS3 remasters via PS Now/cloud), GoW III Remastered (PS4 version), GoW 2018, Ragnarök. PSP titles not natively available.
PC (Steam/Epic): GoW 2018, Ragnarök only.
PS3 (CFW or BC model): Only way to play Ascension, Origins Collection, GoW III original locally.

PS3 Games