You might think that the most expensive book on Amazon has nothing to do with math, but in fact it has everything to do with it. Michael Eisen discovered that in a quest to set the price based on the competitor, two Amazon sellers managed to automatically and unknowingly set the price of a book to $23 million in just a few days.
At first I thought it was a joke â€“ a graduate student with too much time on their hands. But there were TWO new copies for sale, each be offered for well over a million dollars. And theÂ two sellers seemed not only legit, but fairly big time (over 8,000 and 125,000 ratings in the last year respectively). The prices looked random â€“ suggesting they were set by a computer. But how did they get so out of whack?
Amazingly, when I reloaded the page the next day, both priced had gone UP! Each was now nearly $2.8 million. And whereas previously the prices were $400,000 apart, they were now within $5,000 of each other. Now I was intrigued, and I started to follow the page incessantly. By the end of the day the higher priced copy had gone up again. This time to $3,536,675.57. And now a pattern was emerging.
On the day we discovered the million dollar prices, the copy offered by bordeebook was1.270589 times the price of the copy offered by profnath. And now the bordeebook copy was 1.270589 times profnath again. So clearly at least one of the sellers was setting their price algorithmically in response to changes in the otherâ€™s price. I continued to watch carefully and the full pattern emerged.
Once a day profnathÂ set their price to be 0.9983 times bordeebookâ€™s price. The prices would remain close for several hours, until bordeebook â€œnoticedâ€ profnathâ€™s change and elevated their price to 1.270589 times profnathâ€™s higher price. The pattern continued perfectly for the next week.
If you want to read the whole story and the mathematical detective work behind it, go to michaeleisen.org