I checked the Word Games forum to look for threads similar to this one, but didn't find any.

This game is simple. One person asks a "This or That" question such as "Apples or Oranges?", and the next person chooses one and then asks a similar question such as "Black or White?", and a third person chooses either Black or White and asks a similar question, and so on.

So, I start with:

Coffee or Tea?