Well, If you are looking for an answer Can PS4 play PS3 Games Answer is No, you can’t play Game directly by putting an old PS3 disc in PS4. But there is one alternate of that from that you can play the old games.
Ps4 vs Xbox
Let’s talk about Microsoft’s Xbox one which supports old games play but not Sony’s
When we’ve dabbled with backwards compatibility, I can say it is one of those features that is much requested, but not actually used much. That, and I was at a Gran Turismo event recently where they had PS1, PS2, PS3 and PS4 games, and the PS1 and the PS2 games, they looked ancient, like why would anybody play this?
Play PS2, PS3 on PlayStation 4
You cant play directly PS2 and PS3 games on PS4 by putting Game Disc but there is another option for it. Have you heard of PlayStation Now? If No, then it is an online stream from where you can download a library of old games of PS2 and PS3 through the Internet. PlayStation Now gives you a access from where you can play old games from PS2 and PS3. Sony claimed it has chosen more than 500 game titles in this Library by the demand of the Gamers.
PlayStation Now is it worth it?
Playstation Now start it services in UK at 12.99 GBP and in US it starts from $19.99 which is costlier. Its totally up to you if, you have fond of playing old games then it a good deal for you.