This is interesting so I actually developed what should happen instead, mostly. Like where to price for differentiation, clearly undercutting sometimes with a lower price and at other times, when that doesn't make sense, instead raising the price by a bit to end up in an uncrowded price point. Ideally to over time make sense to buy at that price point, with merit, or just being a unique price.

Price is a strong indicator of quality, tells you a lot about clothes when there is no outside reference. Price means that is what the seller will take for the good, a webpage they serve is effectively a call option contract on the webpage when you load it. That's what we determined as a group, the minute bhphotovideo.com loads up a page with a number on it that's a contract to buy at that price--like until there's no stock or until there's a timeout of some kind, the two conditions that got them out of the terms back when the terms were ads on radio. bhphotovideo.com includes terms refusing business on Shabbat, Saturdays, which is uncommon, that also applies and affects things. I think shopping carts work but purchasing doesn't. Webpages about products with prices are call options. Right but not the obligation to buy that good at that price. The seller must honor that price if the right is exercised.

That right lasts perhaps a day, some amount of time to decide without the price going up or down as one thinks about it. On the phone with airlines, you can get a price for a ticket this way, and it's valid until you end the call. Get ahold of the money during the call, and pay it, and it's yours. It can be an hour, it gets stretched out, it is reserved while the flyer is on the phone. The call option has a fixed price, despite the good perhaps fluctuating minute to minute, Amazon prices very keenly. In practice by authorizing the transaction all the pages involved with all the advertising and all the legal language and the pictures, the specs, they all become the terms of the transaction. It seems like there is a lot of liability on the seller's part, and it truly is, it is very competitive, but the number that carries most weight is the price. In the end that price can determine a good deal or a bad deal, or a purchase or losing the purchase to a competitor with lower prices. So in a very crowded market, with say five widgets at $10, and three at 11$, a good currently at $12 must decide carefully--what is the cost of goods sold? If it's low by all means undercut and price at $9, or perhaps $8. Whereas if it costs $10 already, the best is to sell for $13 or so, in a category of its own. And eventually identify that price point's needs and values, what they expect and what better work to justify charging that. But there will be more profits at the higher price point for the latter, the marking up on the one hand and on the other some number of customers will trust it to deserve that price point, whereas charging the same price as 5 other widgets would not work. Critical that the good isn't strictly inferior to the competition, like has or licensed an innovation that gives it at very least a story which cheaper widgets aren't always better, or that it defies the limits of the product category.

So that was going to be a piece of mathematical theory, like give robust and consistent advice on when to undercut and when to instead elevate the product with a unique price. Hey, some people want whatever they can buy with some amount of money they have, others think the game is about buying the middle-of-the-road good, that that is most reasonable. Others will say what matters is the brand or how hot the tech is, if protected that provides a huge margin always, no need to undercut. Instead when they are recognized they can raise the price to be distinguished.

I had it working mostly. Gave consistent answers never got to $23 million books. Kept the prices stable.