As a DM, I have planned a medium encounter for my party of 5 characters.
Before this encounter, as a consequence of some non optimal choices, one of them suffers from 4 exhaustion levels, and there are no ways to remove one or more of them, because they can not take a long rest nor they have prepared a suitable spell such as Greater Restoration.
A total of 4 levels of exhaustion has quite an impact on the combat. The character has disadvantage on all rolls: this is equivalent to the effects of some spells (e.g., Eyebite), but in this latter case there might be chances to deny the spell's effects via a successful saving throw each turn. Moreover, the HPs of the character are halved, which means that they have (roughly) the HP of a character of half of the actual level\$^\dagger\$.
There are several indications about modifying the difficulty of an encounter in the DMG, under the Modifying Encounter Difficulty paragraph in the DMG (pag 84-85):
[...] Increase the difficulty of the encounter by one step (from easy to medium, for example) if the characters have a drawback that their enemies don't. [...] Situational drawbacks include the following:
- The whole party is surprised, and the enemy isn't.
- The enemy has cover, and the party doesn't.
- The characters are unable to see the enemy.
- The characters are taking damage every round from some environmental effect or magical source, and the enemy isn't.
- The characters are hanging from a rope, in the midst of scaling a sheer wall or cliff, stuck to the floor, or otherwise in a situation that greatly hinders their mobility or makes them sitting ducks.
None of the above examples seems to suit the case of exhaustion levels affecting just one character, but they regard situations in which the whole party is facing a severe drawback.
Is there any guidance about taking into account one character with exhaustion levels in computing the encounter difficulty?
\$^\dagger\$ This may suggest to consider this particular character as having half of the actual class levels.