There are numerous game-theoretical (and game-practical in my cases dealing with other sentiences) where you are worse off by having information. The canonical example is the information content of a threat -- you are best off not hearing it so that your threatener cannot expect you to make concessions.

But surely you are better off still if you learn about the threat without letting the threatener know that you have done so? I think we have to distinguish between the information and the public display of such.