Not sure whether anyone is doing it, but an early presumed advantage of internet commerce was that the seller could set a different price for each customer depending on the seller's knowledge of the customer's preferences, socioeconomic status, and other parameters. The global electronic village as the global electronic bazaar!
And you'll often get a discount coupon after staying on a shopping site for a few minutes without interacting.
I’ve tried searching flight prices by remoting into someone else’s computer far away and comparing to mine, and I’ve always gotten the same priced even though I’m not logged in or anything. Ditto for car rentals.
I don’t use travel agents so I can’t say for any other kind of sites.
Maybe sites like Priceline or similar places might do stuff like described, but I very highly doubt airlines do, unless they just don’t show availability in some fare codes to specific customers (which I also doubt, with the possible exception of elite status members).
Unless it’s an opaque rate where you’re bidding for hotel rooms and don’t know which hotel you will get, but you’re forced to buy it once you bid. But I’m talking about publicly advertised prices.
I’ve never even seen a lower price advertised on a third party website compared to the official website of the vendor.
Amazon offers multiple shipping option for various prices.