I have code that does ecommerce price point optimization using machine learning. In an ideal setting, it combines a variety of signals, including prediction using previous sales data. It's also able to "smooth" over different products, so that you can make good price point choices even for products that have very little sales history.
Probably some sort of regression for the prediction part, and perhaps linear programming for the price optimization, since there are probably some nontrivial (but possibly linear?) constraints on pricing.
What would be even more useful is to have the browsing customer's data passed in as a signal as well, but I'm guessing Amazon doesn't send that out to third parties. If 3rd parties could also customize their prices based on the potential of someone to buy (and perhaps offer bundled items based on their own algorithms) we'd probably see even greater efficiencies than we've already seen.
