Game of Thrones Season 6 Discussion [SPOILERS WITHIN]

[Aegon]

There was nothing to gain from killing Bran. Whoever did it did it for personal reasons, and Littlefinger isn't the type of guy to do that. Joff on the other hand definitely is

Littlefinger wants to rule the seven kingdoms.  That can't happen unless he destabilizes the ruling houses by pitting them against each other.  That's clearly what he's up to when he says the knife belonged to Tyrion.  Why can't that be what he's up to earlier, when he hires an assassin and gives him a distinctive knife? 

I still like the theory that Tommen is the perp, but the theory that Littlefinger did it is not unreasonable.

The assassin who was sent was not supposed to be caught by Cat. He started a fire in one of the towers as a distraction. If the plan had worked, the man would have slit Bran's throat and been gone before anyone noticed, along with the dagger.

It makes the most sense to me that it was Joffrey, and when Cat brought the dagger to Littlefinger he quickly used it to his advantage.