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Hi.
You can not check directly who won something nowadays (I much preferred eBay when you could see who was bidding, as well as who won...). But you can use inspired guesswork if you suspect a particular person, as the limited information that eBay provides includes two letter from their alias, and details of their feedback. So you need to know a possible answer, and then you may be able to test your hypothesis...a bit arcane, I'm afraid.
Alan