There is no quick explanation, no one but Amazon knows the algorithm.
Northeastern University did some research on this in 2016. So unless they have changed it, here is what they found (excerpts from a web article at their website):
"New research led by Northeastern’s Christo Wilson, assistant professor in the College of Computer and Information Science, reveals that Amazon is much more likely to feature sellers in the buy box who use an automated practice called algorithmic pricing, even though their prices may be higher than those who don’t. Algorithmic pricing readjusts product prices in real-time using computer algorithms, reacting to variables such as competitors’ changing prices and sellers’ inventory levels…When you go to a page on Amazon, what you’re seeing is typically not the lowest price available,” says Wilson. “For example, we found that 60 percent of sellers using algorithmic pricing have prices that are higher than the lowest price for a given product. Now, 70 percent of the time they only raise the price by $1, but there are many cases where the price increase is on the order of $20 to $60. So you really have to take that extra step and click through to the list of all sellers for a given product if you want to find the lowest price.”…
“When you go to a page on Amazon, what you’re seeing is typically not the lowest price available,” says Wilson. “For example, we found that 60 percent of sellers using algorithmic pricing have prices that are higher than the lowest price for a given product. Now, 70 percent of the time they only raise the price by $1, but there are many cases where the price increase is on the order of $20 to $60. So you really have to take that extra step and click through to the list of all sellers for a given product if you want to find the lowest price.”
“Amazon has a relatively low number of algo sellers—from 2 to 10 percent,” says Wilson. “But they cover almost a third of the best-selling products offered by outside merchants, so the impact is large.”
On average, the prices of about one-third of the products the researchers tracked—333 out of 1,000—changed at least once a day, prices of 170 products changed more than three times per day, and 50 changed more than eight times per day. “The prices of products offered by algo sellers were almost 10 times more volatile than products with no algo sellers,” says Wilson.
Amazon uses its own proprietary algorithm to select who gets in the buy box on any given page at any given time—or, as Wilson puts it, “which seller is going to be ordained and put onto the page.” But he and his colleagues gleaned some hints.
A low price is part of the mix, but so are percentage of positive reviews and having Amazon Prime status. Considering feedback does benefit customers, says Wilson, but there are limits. “Suppose that you have 99 percent positive feedback and I have 95 percent positive feedback. Our research shows that you can charge a significantly higher price than I can and you will still be selected for the ‘buy box. Bottom line, he says, “this is very much a winner-take-all system. If you’re that one lucky seller who gets the ‘buy box,’ you make all the sales. So if you want to be competitive for the top-selling products, you pretty much have no choice: You have to be an algorithmic seller.”