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Certainly in the EU. I am not sure about the Walmart situation though, since something similar is tolerated here (Germany) with the supermarket oligopoly.

Given their size, you can be certain that Amazon is being watched. It's possible they are already running afoul of the rules:

http://ec.europa.eu/competition/consumers/abuse_en.html

Probably "depriving smaller competitors of customers by selling at artificially low prices they can't compete with", since they offer insanely cheap shipping.