Besides not being able to read the Blu-Ray PS3 game discs the PS2 lacks both the hardware and software to be able to play PS3 games.
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No the new PS3 slim can not play PS2 games. To make the PS3 profitable and have it quit selling for a loss Sony stopped making PS3s that could play PS2 games long before the release of the PS3 slim. The only reason you could ever play PS2 games on the first PS3s was the game catalog for the PS3 was next to nothing. Once the catalog of games increased they dropped the ability to play PS2 games.
It is possible to play PS2 games on a PS3 game system. You cannot play PS3 games on a PS2.
PS2 games can not be made to play on a PS3 that does not already play PS2 games
Not any PS3 made for the Past few years. Early models with 4 USB ports could play some PS2 titles. The PS3 Slim does not play PS2 games and all of the Fat PS3 with 2 USB ports do not play PS2 games.
no