Can a Playstation 3 game be played on a playstation 2 console.?

The PlayStation 2 is not capable of playing any games developed for the PlayStation 3. The main reason for this is because the PS3 was developed after the PS2, using new technology. Also, some of this new technology includes the Blu-Ray disc, a disc format used by the PS3 but not by the PlayStation 2.So the PS2 is completely incapable of reading PS3-format discs.

However, the Playstation 3 can play Playstation 2 games.

No, it can't, but some PS2 games can be played on PS3.

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