Illegal in what way? They are not allowed to set prices lower than competitors or raise them at any time?
> Amazon duped his product and sold it at something crazy, like half price
Pricing below an appropriate measure of cost is generally considered predatory pricing. It is very difficult to enforce this, but that doesn't change the fact that it could be illegal and a violation of antitrust laws.
Predatory pricing is illegal in the US, but difficult to prosecute under the existing laws.