Three men went off on a sailboat together, a physicist, a chemist, and an economist. Unfortunately they ran into a storm and the boat was wrecked on an uninhabited island. The only food they were able to rescue from the wreckage was a case of baked beans. As they got hungry, they began to wrestle with the problem of how to open the bean cans. The physicist said "I'll climb a tree and throw a can onto a rock and it'll split open." The others didn't much like this idea because they thought the beans would just splatter everywhere. The chemist said "We can soak the cans in salt water and they'll rust through." The others didn't much like this idea because it would take too long. Then the economist said "Hay--no problem, we'll just assume a can opener."

Economics should always be applied to real life with many caveats. It's been a while since I took my semesters of game theory but here's some brief problems with real life applications.

One dangerous assumption in the hoteling model is that there are no costs to changing your position. That is, the two parties will keep relocating until they're at the Nash equilibrium (neither party can benefit from relocating). This is just plain wrong in real life. Political candidates lose a lot of credibility when they reverse stances on something. It is true that after primaries, candidates then to become more moderate but most other applications of hoteling are dangerous. (Edit: same goes for changing marketing stances, product positioning, pricing... etc.)

Removing relocation/repositioning costs illuminates another unrealistic assumption: there are only two players. If you have huge costs to relocating then you don't want to allow a competitor to come in and take your half of the market because he positioned himself right next to you (i.e. M, N, O). If you add in these two assumptions, players might actually want to have an agreement to separate such that any new entrant would not be able to gain as much profit as they are currently making (while still each controlling 1/2, (i.e. at .33 and .66 on the spectrum or something).

A third assumption is that it is a one dimensional world or that consumers judge choices only along one spectrum. If you add in that another competitors could compete not just on the "beach"... Or if a competitor could differentiate itself on a topic that consumers care about more (not all spectrums made equal)... Or spectrums change, the median consumer could shift from one year to another.

I could go on but the point is to not assume the can opener. In entrepreneurial terms, maybe all the competitors out there are "hoteling," could that be justification to be different? Purple Cow? Or maybe it is better to make a few consumers love you than many to just like you.