What genre is Candy Box, A Dark Room, etc.?

What is the term/genre for games like Candy Box 1/2 and A Dark Room, where there's almost nothing at first but then it grows?

Wikipedia says it's a role-playing game... but... I don't know how they got that.... Anyway, that's too broad a category; I'm looking for a term that's specific to this type of game.

A quick Google search for "candy box genre" led me to this review, which said (not particularly helpfully):

It’s hard to pin down what genre it is too because while it seems fairly RPG-ish, it isn’t, really. But, I’m not entirely sure WHAT to call it, so we’ll just call it “Candy Box!” genre.

So, what's the term or genre for these types of games?

Solution 1:

As far as I'm aware, the umbrella terms for games like these (including less adventure based games like Cookie Clicker) that seems the most popular is incremental games. The best source for these type of games I've seen so far is /r/incremental_games on Reddit.

Solution 2:

We've also seen these games classified as "idle games". (not to be confused with Idle Games Inc.)

Sources:

• XKCD Forum Thread
• IGN: 'Cookie Clicker' and the Idle Game Movement