My girl was looking for a dress for Halloween. Yesterday she found one on Amazon for € 35 and put it in the cart, but did not buy it. Today she looked it up again and it was € 50 so she asked me to look it up with my phone with my Amazon account - it turned out to be € 23 for me, less than half of what it’s for her!
I haven’t seen any studies, I seem to remember there was some news reports many years ago.
I do know that I’ve stood in my living room, on the same wifi, and looked art the same item from Amazon on my phone and my brother in laws phone and seen different prices. But that’s just another anecdote.