At the God of War 2 launch event Cory Barlog unofficially confirmed God of War 3 for the PlayStation 3. Barlog did confirm that God of War 3 will run at the highest possible HD resolution, 1080p, and the game will support SIXAXIS tilt and vibration functions.
Barlog also confirmed he is looking into a cooperative mode for a next God of War "if we can do something unique with it."
And last but not least, Sony finally officially confirmed God of War for the PlayStation Portable. The game won't be a port.
"It is its own story that connects to the overall story. God of War, God of War 2, and then if all the stars align God of War 3 will be the telling of a trilogy. This PSP story will be a further fleshing out," Barlog confirmed.
Barlog also confirmed the game will be big and epic, and it will be a real God of War game, so no reusing levels from the PlayStation 2 God of War games. They are still looking at a good solution for losing the second analog stick, which was used for rolling in the PlayStation 2 games.
There were no confirmations about any connectivity between PSP and PS2/PS3. Furthermore, they only found out about PlayStation Home at GDC as well.
Keep checking PSU.com for the latest God of War news.