What's the explanation for people's apparently irrational bidding schemes on eBay? I don't understand why almost everyone, myself included at times, will place an initial bid on an item that's lower than what they're actually willing to pay and then watch the item like a hawk as it nears the end of the auction and continually up their price if they get outbid. There's no reason to get into a bidding war on eBay, since the system automatically increments your bid as necessary up to your maximum. The only reason to continually up your bid near the end of an auction is if the price you're willing to pay keeps rising... but why would that be the case? Because there's some pride in winning, or because you misjudged your maximum price earlier? In either case, it seems the wise thing to do would be to stick with your earlier, less impassioned maximum.
However, there's at least one instance in which I can imagine rationally wanting to increase a bid: if you're bidding on multiple similar items. You may not want to put in high bids at the beginning because you won't want to win all the items at high prices, but as you start to lose some items you can increase your bids on the remaining items to increase your chance of winning at least one.
Anyway, I generally try to exert self-control and not increase my initial bid when someone tops it. Yes, I want to win, but the item doesn't suddenly become more valuable to me just because someone outbids me. I open with the highest price I'm willing to pay and let eBay increment the price up to that level. If I lose, I lose because the price went above my estimation of the item's value.