Which means "I want to beat you, but I don't care whether I win the auction or not."

I don't quite understand that statement. "Beat me" as in raising the bid as high as they can, whether or not they win the auction?
IMO, most people think eBay is the land of cheap stuff. People will constantly increase their bids by the minimum increment until they reach their max price. In other words they are looking for a deal by trying not to pay what they think is a fair price, and don't get the proxy bid concept.