competitor analysis, sometimes called competitor research, is a commonplace activity in industry and commerce (and between nations) but still seems to suffer from a bad press in academia – rather like Activity Based Costing or Business Process Re-engineering.
Nevertheless, its use is not uncommon in universities (and more common in colleges), even if not many faculty-based academic staff are aware of that. The less commonly used phrase "comparator research" is fact better as it makes clear that the research should extend also to those who are not direct competitors of an institution.
For a short description of how to use it within a benchmarking context, see the Pilot Phase report on competitor analysis. This is an extract from the full Final Public Report on Pick&Mix and eMM institutions, but there is no particular reason why it should be used only in Pick&Mix benchmarking.