Because of an inadequate lack of attention regarding conference deadlines on my part, I find myself currently reading lots of papers while concurrently serving on the SPAA and ICALP Program Committees.
And somehow, this means I'm reading lots of papers with competitive analyses of algorithms. (Both the standard variety, and the more new-fangled but generally similar "price of anarchy" variety.) Looking back on it, I should have simply have told the PC chairs that it might be best to make sure not to assign me any such papers, as I'm not sure it's fair to the authors who get me as a reviewer.
OK, I'm exaggerating. Don't get me wrong; I'm not automatically assigning negative scores to any such paper. Some of these papers I really like. But in general, as I've expressed frequently elsewhere, I'm a skeptic when it comes to competitive analysis. Why exactly should anyone care that you have an algorithm that in the worst case always gets within a factor of 6.5 of the optimal solution possible? Why is that the right way to judge an algorithm? (Never mind the offshoots, like those where you have an algorithm that's competitive if it has twice as much as memory as you allow for the optimal algorithm, and so on...)
In my mind, the problem is that competitive analysis has become such a standard in Theoretical Computer Science that people don't feel the need to bother justifying anywhere in the paper why they should use competitive analysis, when in fact these papers scream for a need for motivation.
Here are some motivations that tend to work for me when reading competitive analysis papers.
1. The resulting problem is just so mathematically interesting that we really have to look at it. (One person I can think of that manages to pull off this motivation with me time and again is Susanne Albers.) Generally, to pull off this motivation, your problem should be simple, clean, and natural; if you start to bog down in details, claiming that you're giving a "more realistic" model of the problem, you've already missed the boat in my mind. (If you really wanted to be realistic, you wouldn't be using competitive analysis...)
2. You are considering the performance of real, existing algorithms. This seems reasonable to me; here's something people actually do (like, say, Shortest Job First scheduling), and you want to gain some insight into its worst-case performance for this notion of worst-case. Many price-of-anarchy results actually correspond to the behavior of reasonable algorithms one might consider in practice, so I admit I often find myself more sympathetic to Price of Anarchy results, which seem more motivated.
3. You are using competitive analysis for an essentially (complexity)-theoretical result.
4. You are using competitive analysis to gain significant insight into the problem (and algorithms for the problem) that could be useful in understanding real performance or designing real algorithms. I think most papers implicitly claim that their paper fits into this last category, just because it obviously doesn't fit into the other three, but usually this isn't explicitly discussed. I think this motivation works best when the problem is inherently very hard.
I'm sure there are other reasonable motivations. But overall I would call for more restraint from the community; not everything should be subjected to competitive analysis, just because it can.