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In a conversation with journalists, the President of Sony’s Worldwide Studios said that PS3 games - both the retail and downloadable variety - will not be compatible with PlayStation 4, at least not natively. In other words, your PS3 discs won’t work with the new console, neither will any games you downloaded. This means that titles like Journey, The Unfinished Swan, Shatter, and hundreds of other games available in the digital space will not be carried over to PlayStation 4, in addition to the collection of PS3 discs you already have.
However, you *will* be able to play PS1, PS2 and PS3 games on the PlayStation 4 by downloading them. The PlayStation 4 will include the services Gaikai. They offer cloud storage, and this is where you will most likely buy your old games from. The bad thing is, if you already own a game and you want to play it on the PS4, you will have to buy it from the online store in order to play it.
“There are two ways to play legacy content: emulation, or cloud services from Gaikai. But native support of digital games from PS3, no, sorry. It doesn’t work.”
~ Source