The OP suggests a sealed bid auction. That means they wouldn't know how much other parties have bid. There would be no way to guarantee they've put in the highest bid.

In a sealed bid, second price auction, Amazon could just bid approximately infinity every time, and only pay the second highest bid.

(Presumably, they wouldn't actually bid infinity, just in case someone else bids infinity-1 as a joke. But they could afford to bid what the Amazon brand is actually worth to them.)