Sony said it could happen, and it has.
As part of the SOE Live 2014 event, Sony Online Entertainment has confirmed that the free-to-play zombie adventure, H1Z1 , is headed to the PlayStation 4. This comes after SOE president John Smedley said back in May that a PS4 version was definitely possible.
We don't have a release date just yet, but at least we know it's coming. The game was inspired by DayZ and The Walking Dead and it'll launch for PC via Steam Early Access later this year. There's no concrete for that one, either, so it's feasible that the PS4 and PC iterations will come out around the same time.
SOE also announced that another free-to-play multiplayer game, PlanetSide 2 , will launch later this year, also as an Early Access game. If you don't mind the controversial F2P model, you should give these games a try.
Related Game(s): H1Z1