I'm not sure I buy this because even if a third competitor entered and claimed nearly half of the market, the people far out in the tail of that claimed half would not experience any improvement in service. To them, they would be nearly just as bad off.
You're missing my point. A rational duopoly which is concerned about the possibility of a third competitor entering the market will avoid satisfying Hotelling's law. It isn't the third competitor entering the market which improves things; it's the threat of a third competitor entering the market.
I understand that regulations present their own problems: what stops the duopoly from purchasing regulatory capture and raising barriers to entry?
That's a political problem, not an economic one. ;-)
I don't think I missed your point. I think I said that a rational duopoly won't bother worrying about what economical solution best prevents a third entrant, when there is always the possibility of simply paying from established wealth to compensate a would-be entrant for their willingness to not enter.
I don't see it as a political problem. It's such a ubiquitous part of any real market that I just see it was a way in which typical econ toy problems fail to correspond to reality and fail to produce useful predictions. It's like trying to use Newtonian physics when quantum effects really matter, except you've got so many economists employed because of the Newtonian-like toy models and they have a real need to keep hand waving and trying to convince everyone that the Newtonian approximations matter, that deriving theoretical results like this matter to "build intuition" or "create the mathematical framework" or whatever, but it's just clearly not true or useful to anyone but those researchers themselves.
You're missing my point. A rational duopoly which is concerned about the possibility of a third competitor entering the market will avoid satisfying Hotelling's law. It isn't the third competitor entering the market which improves things; it's the threat of a third competitor entering the market.
I understand that regulations present their own problems: what stops the duopoly from purchasing regulatory capture and raising barriers to entry?
That's a political problem, not an economic one. ;-)