We were playing the level seven scenario out of the core box and flipped into the treachery card Caught in a Web . We had two (of four) players tied for highest threat level. Does Caught in a Web resolve ? And if so, how?

Card text...
When Revealed: The player with the highest threat level attaches this card to one of his heroes. (Counts as a Condition attachment with the text: "Attached hero does not ready during the refresh phase unless you pay 2 resources from that hero's pool.")

If there is a tie, the players get to choose who is the lucky winner. I don't know who gets the official authority for the decision (first player probably), but hopefully the group can reach a consensus.

Yeah, in the case of ties, the first player gets to choose. However, with cards like Caught in a Web, there is often a character that is the "best" choice so often the group will agree to attach it to that hero.