My Nightmare - Or Yours?: If an opponent wins the roll to determine the first player and does not choose Nightmare's controller to be the first player, characters on that opponent's force modify their attack values by -1 as long as Nightmare is on the map.

Feed on Your Fear and Despair: Once per turn, when an opposing character takes pushing damage, you may heal Nightmare 1 click.

Your Mind Betrays You: Nightmare can use Penetrating/Psychic Blast. When he does, modify his attack value by +1 for each action token on all target characters.

Do I have to tell my opponent about the trait My Nightmare - Or Yours?
No. You are not required to warn them. That said, please keep the two following things in mind:

1) Some may view not telling your opponent ahead of time as being very unsportsman like. In an official tournament setting, this could perhaps even cause you to lose out on the Fellowship prize.

2) Absolutely nothing prevents your opponent from requesting to see your character cards before the game begins. So, if your opponent is wary of characters he/she has never seen before, they will likely ask something along the lines of "Hey, what does Nightmare do?" And if they do ask, you are required to share any public information with them, including allowing them to read Nightmare's card. You can't deny this request. (And, in all honestly, all players should ask at the start of every game to see the opposing cards... you certainly are not expected to have everything memorized, and familiarizing yourself with what your opponent is about to throw at you is a VERY good idea.)

So, yes, you may catch a player with their pants down, so to speak. But it may be looked upon unfavorably by others and there is absolutely no way to "surprise" a player that specifically asks to know what is up with Nightmare.