The following is called "proxy bidding" and is allowed by eBay (we have over 500 transactions at the moment)

This is from the eBay site itself:

1. When you place a bid, you enter the maximum amount you'd be willing to pay for the item. Your maximum amount is kept confidential from other bidders and the seller.
2. The eBay system compares your bid to those of the other bidders.
3. The system places bids on your behalf, using only as much of your bid "as is necessary" to maintain your high bid position (or to meet the reserve price). The system will bid up to your maximum amount.
4. If another bidder has a higher maximum, you'll be outbid. BUT, if no other bidder has a higher maximum, you win the item. And you could pay significantly less than your maximum price! This means you don't have to keep coming back to re-bid every time another bid is placed.
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One personal example....I found a vintage doll on eBay last year. Starting bid was $40. I knew that the max I would want to pay is $100. I ended up paying $65 because the final bids were only up to $64 or something like that.

I know people who set their watches to monitor the last few minutes of an eBay auction, just in case they might be outbid...you just never know.

Good luck bidding, all!