Ps doesn't have a network for each system correct?

So people on ps3 can still play with ps4 or nah.

Depends on the game but most of the time games are not cross-platform.

while PSN is shared it varies from game to game if they allow cross platform

Ah OK wasn't clear on this.

So big name games like cod or somthing like that would t cross platform

i'd imagine theya ren't but i don't play CoD so I can't answer that
I do believe FF14 is cross platform for PC, PS4, and PS3, but this is the only game i can think of that is like this

skullgirls is cross platform between ps3 and ps4


thats the only game that comes to my mind, for the most part, majority of games aren't cross plat

OK figured it would be only games that have a small community so reaching across platforms is the only way to keep it up

i think Final Fantasy (whichever one the new online is) is one of the few games that's cross platform

And i guess skullgirls whatever that is