In an interview with Naughty Dog Creative Director, Neil Druckmann and Game Director, Bruce Straley Gaming Examiner explores the world of The Last of Us. While they hit on various facets of the game design and how it relates to Uncharted, there is a brief mention of the multiplayer and how that is going to factor into the mechanics.
Now I wouldn’t rule out co-op entirely based on this one statement. Uncharted’s co-op never actually took place in the main campaign either. Instead they were a series of spin-off missions involving many of the characters from the franchise.
As for competitive multiplayer, with Naughty Dog’s focus being “a very tight, well-constructed, narrative-driven gaming experience”, it seems unlikely. Then again, Mass Effect 3 had multiplayer, so anything is possible. What would you g1s prefer co-op or competitive multiplayer?