Fight fire with fire and snipe yourself.
Just remember that regardless of when your bid is placed, it still has to be the highest to win. EXCEPT, when 2 bids are the same or there isn't enough difference between them to meet ebay's minimum bid increment. In that case, the 1st one in wins.
So, if people were completely rational, the best strategy would be to bid on an item the second it is listed. I'd stick with the sniping strategy.
(Automated) sniping is a timesaving convenience for people that want to avoid drawing early attention to an auction item, 'nibbling' bidders (bidders who have no max in mind, bidding the minimun increment over and over until they're the high bid), and competitive emotional bidders and bidding wars that come with them, all of which normally result in a higher final price. If you have the time, you can do it manually.
http://www.hidbid.com is a good sniping service to use, it is web based, so you don't need to worry about leaving your computer on for your bid to be placed.
If for whatever reason you do not like the idea of sniping, decide on your absolute maximum bid, and place it. If you win, great. If you lose, the winner paid too much as far as you are concerned. Bid once.
Make sure you're eligible to bid on an item before scheduling a snipe (or doing it manually), so that your bid will be accepted. As long as you live in a country that the seller ships to, you don't have many (or any, I think as little as two within the past six months can get you blocked) unpaid strikes lately, and you have enough positive feedback, you should be ok. If you have a problem with one of those things, you could contact the seller and ask them to accept your bid, as long as you know early enough.
A couple more benefits of sniping:
1. Sniping is actually a way of combatting shill bidding - when the seller or his buddy bids on the item until they're the high bid, and know your max, then retract their bid, and use yet another account to bid on the item, bidding just below your max. You don't give the shiller time to retract their bid in order to leave you as the high bidder, close to your max. You can't do much about a shill bidder letting their bid ride to the end of the auction, if it just raises but doesn't exceed yours.
Also, look out for 2nd chance offers, as they would be a reason for the shiller to let their shill bid ride, you may want to decline any and look for a different seller with the same item. Unless of course, the price seems ok with you, even though possible artificially jacked up.
2. You can just cancel a snipe with as little as five minutes left (I guess depending on which service or software you use) in an auction, if you change your mind about bidding on an item, and your bid won't be placed. If you place a bid on ebay and then retract it (not a seller's or ebay's favorite thing), you can be blocked from bidding on other auctions after doing this a few times, not sure what that # is.
Here's a couple links to pages for eBay bid increments:
http://pages.ebay.com/help/buy/bid-increments.htmlhttp://pages.ebay.co.uk/help/buy/bid-increments.htmlhttp://pages.ebay.de/help/buy/bid-increments.html