You're citing the opinion of two senior faculty who are basically no longer publishing in economics. Make of that what you will.
I'm interested in doing theory and choosing between a few schools: Cornell, Rochester, UCSD, Caltech. It seems like Cornell has some people ( e.g. Larry Blume and David Easley) doing stuff on CS-Econ, algorithmic game theory, and networks. I don't know much about that stuff but I was told they are hot topics. Are those actually hot topics or are they just saying that?
Yes and no. These are the types of work that will be done in computer science department or collaboration between computer science department and economics department. In economics department, I wouldn't say that algorithmic Game Theory is a popular field.
By "make of that what you will" I mean something like "use that information depending on your individual preferences".
Factors for you to consider are (/were) the following:
1. Do you want to publish in finance or place into finance? Easley's output seems so geared towards finance right now that I'd even say he might not add value as a member of your dissertation committee if you're going for pure theory. Could be wrong though; you'll have to judge by yourself if you ended up taking the Cornell offer. Blume is still a theorist in some sense, but he's the less active of the two.
In comparison, it seems that Toda at UCSD, and Caltech as a whole, have research interests that share some similarities with the above, but can find a decent audience in econ outlets.
2. Are you asking because you want to work with these two faculty, or as a marginal consideration? If the former, it's usually a bad idea to select any program based on 2 senior faculty that are near retirement. Blume and Easley are both active for their age, but it's difficult to judge when they might retire.
3. Is the subfield actually expanding in a way that's relevant to your career? The answer probably depends on your career inclinations again. Easley et al's work has been influential, but it's not clear if they're developing the core of a new field, or picking off relative low-hanging fruits. Or something in between - e.g. these works might lead to lots of papers in econometrics or empirical micro, not a trend that you could exploit with your expected skill set.
The complexity stuff also has relatively more influence in European departments (as is the other half of Easley's work, market microstructure). But the U.S. top 5 econ departments haven't really hired someone with explicit comp-sci training or background, and a few notable professors who seemed interested in network and complexity actually seem to be shifting away from it. For the most part, I think this is a relatively stagnant area in economics departments. So if you think you're most likely to end up as a "standard" game theorist or decision theorist in the end, going into Cornell to work with these two wouldn't seem to me to be optimal ex-ante.
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