Russell Impagliazzo published "A Personal View of Average-Case Complexity" (preprint) back in 1995. He presented five possible worlds we could be living in, depending on how P and NP were related. The first world presented is Algorithmica, in which P = NP, "or some moral equivalent" such as NP being contained in BPP, or NP = RP ≠ P. The remaining four worlds are all variants where P ≠ NP, and they are "morally" different, with differences between the algorithmic applications of hardness differntiating the worlds.
It seems to me that there is a large landscape inside Algorithmica, and I'm wondering:
has anyone written about Algorithmica in more detail?
The best reference I have found so far is a blog post by Richard Lipton from 2009 which briefly explores Algorithmica but doesn't go into much detail.
Although it seems unlikely that we are living in Algorithmica, understanding that landscape might still motivate interesting work. For instance, it might highlight precisely what the world would have to look like for quantum factoring to be rendered irrelevant, or if quantum factoring is ignored, where classical factoring might still be challenging. See the related question Status of Impagliazzo's Worlds? for a discussion focused on the other parts of the landscape, including Boaz Barak's summary of a 2009 workshop about Impagliazzo's multiverse.