If I put my maximum on eBay, it leaves me vulnerable to anyone who wishes to discover my maximum. All that another eBay member needs to do is bid some ridiculous price that is sure to be above a genuine maximum; that reveals the maximum bid of the underbidder (me). Then the eBay member would retract the bid.
If the bidder is the seller with a shill account, s/he can wait until not long before the end of the auction, and place a bid just below my maximum. That would result in my having won the item at a higher price than I would have paid had the seller not known my maximum.
If the bidder is another potential buyer, s/he knows just how much I'm willing to bid, and if they want to, they can now either bid just above my maximum in the last few moments of the auction, or bid just under my maximum, out of whatever motivation a fellow collector in some narrow fields might have. I'd either lose unfairly because of the other buyer knowing my maximum through underhand tactics, or I'd be paying my absolute maximum unfairly, with the other buyer not having made a genuine bid with the intention of winning but rather to force up the price.
My absolute maximum is the highest price I'm willing to pay, but it's certainly not the price I'm hoping to pay. If I had to pay my maximum every single time, I'd have to cut down my collecting drastically. The nature of online bidding on eBay is such that I have every right to keep my maximum secret, and so far I've won items at considerably less than my maximum. Thank God. Sometimes my maximums are outrageously high. At least if I lose an auction, I know that I lose fairly.
Oh, and another reason to avoid putting automatic bids in place with a maximum on eBay is to avoid nibble-bidders driving up the price.
