Machine learning for dynamic pricing I haven't been able to find a good answer for this (though I know that there are a few related questions):
How does Amazon determine how to price a product? How does it figure out when to downprice, and by how much? I'm sure that there's some machine learning involved here, but what does it involve?
Doesn't have to be Amazon.
I have metadata and data on past demand, but a regression model and random forest neither showed that anything other than overall sales are significant. I also have a natural experiment, but I don't want to base my whole case on one limited time period.
 A: "Hey guy, what is the ultra-secret recipe of coca-cola ?". 
I don't think you will get a precise answer.
I think it is a very complex and well optimised process, I don't have any other clue. I can only imagine that it is very far from a supply and demand process (in the basic economical sense). 
It will depends on stocks, localisation of stocks, price to move stocks, price of oil, price of suppliers, contracts with transport companies. You may also add reviews, the price of other item bought with it, the price of other item bought by customer who bought the item, the money generated by advertising.... Who knows ? Macro economics datas ? Rumors on the market ? Laws to be passed ? All these data can have an influence over price, their past values and their forecasting too (this can be genralized to their financial contracts and derivatives). I am pretty sure that they learn patterns over that. That's all... the rest is in the mind of 10 (maximum) research/risk manager at Amazon an I think that only the head of their research departement has the whole picture...
Edit: I forgot the irrationnal parts of building price such as "10.01 is expensive, you know what is nice ? 9.99" or " - It's too expensive, the price should be lowered. - why ? -because I said so !"
A: I have no idea but I can guess based on how I would do it.  I would take a reinforcement learning approach.  Essentially, have an agent that takes an action (to decrease or increase the price of an item) based on the observed state of the system (traffic, season, other factors idk...) and the agent would then get some sort of reward (sales, margin, idk...).  So some kind of simulation (or actual experiments) would occur in which the agent would learn the optimal price policy to take given the state that it is in in terms of maximizing reward.  This is analogous to the bandit problem since some sort of pricing exploration has to be done initially.  I can't really assume that this method would be tractable though (millions of items!) 
