I will assume that there are three strategies to choose from:
1 – Bid the maximum price you are willing to pay at the start of the auction and then wait for the auction to close. I will call this strategy Maxing
2 – Increase your bids in the smallest increments possible until you reach your maximum or just overtake the second highest bidder. I will call this strategy Increments
3 – Wait until right at the end and then bid the maximum that you are willing to pay. I will call this strategy Sniping
These are all strategies that can be seen on eBay.
If everyone followed Maxing and just bid once at their maximum value then eBay would become a lot simpler. If you knew that everyone else was going to play Maxing then whether you play Maxing, Sniping or Increments will make no difference. You will get to your maximum bid one way or another and then either win at a price less than your maximum, or you will lose but not pay more than your maximum. Maxing would be the easiest way to do it because you just make one bid and don’t have to time it for the end of the auction.
If you suspect that others are not going to follow Maxing, and are instead going to play Increments, then what strategy should you play? If you play Maxing then you will win if your bid is higher than they are prepared to pay and you will lose if they are prepared to pay more. This is still efficient for you, but is Sniping better?
If you Snipe against someone playing Increments then you do not give them time to get all their bids in to reach their maximum. This means that Sniping may give a better result against Increments than Maxing does.
The third situation is if you think others are going to play Sniping. Then what should you do? Maxing will be fine against Snipers, but Increments will be inefficient because you will not get time to make enough bids to overtake the Sniper. Sniping against another Sniper will also be fine, whoever has the highest valuation for the item will win it.
We end up with a situation where if everyone played Maxing then it would be easier to also play Maxing, so everyone Maxing would be an equilibrium. Maxing is also fine against Sniping as well but as soon as someone starts playing Increments then Sniping becomes better than Maxing.
In a perfect world everyone would play Maxing, but since they don’t the best strategy is Sniping. Interestingly, most people on eBay seem to use either Increments or Sniping, it is rare to see someone make a single bid early in an auction and not return.
One of the reasons this happens is because people don’t actually always know their valuation for an item. They are influenced by the other bids. Players use the Incremental strategy because they are unsure of their true valuation and are seeking out information from other bidders.
Sniping is the best strategy on eBay because it doesn’t give away information and influence other bidders in the way that other strategies do, but if you can’t be around for the end of the auction then Maxing is a pretty good alternative.