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As a strategy person, I would like to add the followings:
1.) The program at Northwestern is strong, well regarded, but not in the same area as the usual "strategy" departments would participate. It is really more of an econ shop than a strategy shop.
2.) NYU is strong, has many excellent faculty members, but is not necessarily a place to focus on strategy per se. There is nothing wrong with that, strategy as a business sub-field does not necessarily have a clear boundary. Many strategy people are doing stuffs pretty much similar to the "management" people are doing.
3.) I would offer a bit of a push-back on the notion that game theory is one of the two main approaches in strategy. Clearly there are the econ vs. sociology (OT) streams in strategy research, but the econ approach does not usually resort to game theory. If you review the top strategy journal (SMJ), what people mean by the econ stream in strategy usually means heavy use of econometrics methods, not necessarily econ theory like game theory. In fact, many prominent economists in strategy field have been crying for a stronger "theory" orientation in the field. Game theory, in particular, is now rarely used in strategy (in the sense that an econ publication revolves around the core concept of game theory, many strategy journal articles appeal to game theoretic logic, but offer no proof, or reserve the proof at the appendix section, and would not bother dwelling on the heavy math stuff).
This impression that game theory might be heavily used in "strategy" might be rooted in the fact that econ people do use the term "strategy" as well in their literature, but if you look at the type of research covered, it's only tangentially related to what people in "strategy" would be doing.
From my own experience, "strategy" in business school deals with the following main topics: transaction costs economics (Coase, Williamson approach, while heavily microecon based, but few in this stream use heavy math. most paper, i.e. Williamson's classics, are mostly just English text), resource based view (Jay Barney, Rumelt, etc, again, while some papers appeal to econ reasoning, it is hard to see the kind of heavy math in the usual econ literature.), knowledge-based view (as an outgrowth of resource based view, many would even consider it part of the RBV), many prominent researchers blend these approaches together into unique approach that is perhaps hard to classify at first, for example, Mintzberg's papers are usually case studies, English text only, but certainly are important papers in the field of strategy.
The key distinction is that when strategy people say their research is "econ based," it might or might not necessarily mean a heavy game theoretic, or even microecon type of research. This presents a bit of a problem for program like Northwestern's. Most likely graduates from that program compete for publication in econ journals (indeed I have yet to see people from that department publish in the typical top strategy journals), and in that arena, it's extremely heavy in rigorous math. It is somewhat unfortunate they use the term "strategy" in their department name (not that I would like to monopolize the term for my own field), as it creates a bit of a confusion for people who aspire to pursue a career in this area. I would recommend thinking of that department as pure econ shop instead.
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