How to start doing research on the economics of AI?

I'm entering my 2nd year PhD at a top-10 US economics dept, and I'm interested in the economics of AI. The field seems scary big, with lots of new papers coming out, with people like Goldfarb, Gans, Agarwal, Alex Imas, Erik Brynjolfsson, Sendhil Mullainathan, and ofc Acemoglu, among several dozen other top economists contributing regularly to the field.

Is there a structured way to become familiar with the literature and the main questions and models that are being used in this sub-field right now?

Separately, I also want to know if I should seek any additional training before trying to write papers in this field. I have a relatively solid math and econ background: lots of calc/real analysis/diff eqns, all the graduate econ courses, though I could be better with linear algebra. I have never taken a formal CS course, I only audited UC Berkeley's INFO259 (NLP), so does anybody have recommendations on what parts of CS/AI I should focus on learning? Ultimately, I intend to write economics papers on AI, but it's still very useful to learn the underlying technical aspects of AI. I just don't know where to start.