Imagine that everyone in the world has a bizarre relationship with the truth and sleep. Everything they believe while asleep is false, whereas everything they believe while awake is true.

Consider Sting and Fiona.

Sting believes that Fiona believes that Sting is asleep.

Fiona believes that Sting is asleep.

Is Sting awake or asleep?

Is Fiona awake or asleep?

Sting is awake; Fiona is awake

Explanation:

Since everything they believe while awake is true, both Sting and fiona are awake because Sting believes that Fiona believes that he is asleep, and Fiona believes that Sting is asleep: they just believe, in other words, they think those situations are true, correct, or real - - they don't dream about them - - so they are awake.